Time-delay systems: An overview of some recent advances and open problems

Automatica

Volumn 39, Issue 10, 2003, Pages 1667-1694

  Richard, Jean Pierre ^a  

^a ECOLE CENTRALE DE LILLE   (France)

Author keywords

Aftereffect; Dead time; Delay systems; Functional differential equations

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; INFORMATION TECHNOLOGY;

TIME DELAY SYSTEMS;

CONTROL SYSTEMS;

EID: 0041511967     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(03)00167-5     Document Type: Article

References (272)

1. Abdallah, C., Birdwell, J. D., Chiasson, J., Chupryna, V., Tang, Z., & Wang, T. (2001). Load balancing instabilities due to time delays in parallel computations. In Third IFAC workshop on time delay systems, Sante Fe, NM, December 2001.
2. Abdallah, C., & Chiasson, J. (2001). Stability of communication networks in the presence of delays. In Third IFAC workshop on time delay systems, Sante Fe, NM, December 2001.
3. Abdallah, G., Dorato, P., Benitez-Read, J., & Byrne, R. (1993). Delayed positive feedback can stabilize oscillatory systems. In ACC'93 (American control conference) San Francisco, (pp. 3106-3107).
4. Aernouts W., Roose D., Sepulchre R. Delayed control of a Moore-Greitzer axial compressor model. International Journal of Bifurcation and Chaos. 10(2):2000;1157-1164.
5. Aggoune, W. (1999). Contribution à la Stabilisation de Systèmes Non Linéaires: Application aux Systèmes Non Réguliers et aux Systèmes à Retards. INRIA/CRAN, University of Metz, France (in French).
6. Ailon A., Gil M.I. Stability analysis of a rigid robot with output-based controller and time-delay. Systems and Control Letters. 40(1):2000;31-35.
7. Akian, M., Bliman, P. A., & Sorine, M. (1998). P.I. control of nonlinear oscillations for a system with delay. Research report 3422, INRIA, May 1998.
8. Al-Amer, S. H., & Al-Sunni, F. M. (2000). Approximation of time-delay systems. In ACC'00 (American control conference), Chicago, IL (pp. 2491-2495).
9. Artstein Z. Linear systems with delayed controls. A reduction IEEE Transactions on Automatic Control. 27(4):1982;869-879.
10. Åström K.J., Hang C.C., Lim B.C. A new Smith predictor for controlling a process with an integrator and long deadtime. IEEE Transactions on Automatic Control. 39(2):1994;343-345.
11. Banks H.T., Kappel F. Spline approximations for functional differential equations. Journal of Differential Equations. 34:1979;496-522.
12. Banks S.P. Nonlinear delay systems, Lie algebras and Lyapunov transformations. IMA Journal of Mathematical Control and Information. 19(1-2):2002;59-72.
13. Bartholoméüs A., Dambrine M., Richard J.P. Bounded domains and constrained control of linear time-delays systems. JESA, European Journal of Automatic Systems. 31(6):1997;1001-1014.
14. Battle C., Miralles A. On the approximation of delay elements by feedback. Automatica. 36:2000;659-664.
15. Beghi A., Lepschy A., Viaro U. Approximating delay elements by feedback. IEEE Transactions on Circuits and Systems. 44:1997;824-828.
16. Belkoura, L., Dambrine, M., Richard, J.-P., & Orlov, Y. (1998). Sliding mode on-line identification of delay systems. In VSS'98, Fifth international workshop on variable structure systems, Longboat Key, FL, December 1998 (pp. 230-232).
17. Belkoura, L., Richard, J. P., & Orlov, Y. (2000). Identifiability of linear time delay systems. In Second IFAC workshop on linear time delay systems, Ancona, Italy, September 2000 (pp. 173-176).
18. Bellen, A., & Zennaro, M. (2001). A free step-size implementation of second order stable methods for neutral delay differential equations. In Third IFAC workshop on time delay systems, Sante Fe, NM, December 2001.
19. Bellman R., Cooke K.L. Differential difference equations. 1963;Academic Press, New York.
20. Bellman R., Cooke K.L. On the computational solution of a class of functional differential equations. Journal of Mathematical Analysis and Applications. 12:1965;495-500.
21. Biberovic, E., Iftar, A., & Ozbay, H. (2001). A solution to the robust flow control problem for networks with multiple bottlenecks. In 40th IEEE CDC'01 (Conference on decision and control), Orlando, FL, December 2001 (pp. 2303-2308).
22. Blanchini F., Ryan E.P. A Razumikhin-type lemma for functional differential equations with application to adaptive control. Automatica. 35(5):1999;809-818.
23. Bonnet C., Partington J.R. Stabilization of fractional exponential systems including delays. Kybernetika. 37(3):2001;345-354.
24. Bonnet C., Partington J.R., Sorine M. Robust control and tracking of a delay system with discontinuous nonlinearity in the feedback. International Journal of Control. 72(15):1999;1354-1364.
25. Bonnet C., Partington J.R., Sorine M. Robust stabilization of a delay system with saturating actuator or sensor. International Journal of Robust and Nonlinear Control. 10:2000;579-590.
26. Borne, P., Dambrine, M., Perruquetti, W., & Richard, J. P. (2002). Vector Lyapunov functions: Nonlinear, time-varying, ordinary and functional differential equations. Stability and control: Theory, methods and applications (Martynyuk ed.) (pp. 49-73). London: Taylor and Francis.
27. Boukas, E. K., & Liu, Z. K. (2002). Deterministic and stochastic time-delay systems. Control engineering. Basel: Birkhauser.
28. Brethé, D. (1997). Contribution à l'Etude de la Stabilisation des Systèmes Linéaires à Retards. IRCCyN, University of Nantes, EC Nantes, France, December 1997 (in French).
29. Bushnell L. Editorial: Networks and control. IEEE Control System Magazine. 21(1):2001;22-99. (special section on networks and control).
30. Byrnes C.I., Spong M.W., Tarn T.J. A several complex variables approach to feedback stabilization of linear neutral delay-differential systems. Mathematical Systems Theory. 17:1984;97-133.
31. ∞ control of uncertain markovian jump systems with time delay IEEE Transactions on Automatic Control. 45(1):2000;77-83.
32. Chang P.H., Lee J.W., Park S.H. Time delay observer. A robust observer for nonlinear plants ASME Journal of Dynamic Systems Measurement and Control. 119:1997;521-527.
33. Chang, P. H., & Park, S. H. (1998). The enhanced time delay observer for nonlinear systems. In 37th IEEE CDC'98 (Conference on decision and control), Tampa, FL, December 1998 (pp. 367-368).
34. Chen J., Latchman H.A. Frequency sweeping tests for stability independent of delay. IEEE Transactions on Automatic Control. 40(9):1995;1640-1645.
35. Cheres E., Gutman S., Palmor Z.J. Stabilization of uncertain dynamic systems including state delay. IEEE Transactions on Automatic Control. 34(11):1989;1199-1203.
36. Choi, H. H. (1999). An LMI approach to sliding mode control design for a class of uncertain time delay systems. In ECC'99 (Fifth European control conference), Karlsruhe, Germany.
37. ∞ controller design for linear systems with delayed state and control Automatica. 31(6):1995;917-919.
38. ∞ controller design for state delayed linear systems Automatica. 32(7):1996;1073-1075.
39. ∞ controller design for linear uncertain time-delay systems Automatica. 33(9):1997;1749-1752.
40. Choi S.B., Hedrick J.K. An observer-based controller design method for improving air/fuel characterization of spark ignition engines. IEEE Transactions on Control Systems Technology. 6(3):1998;325-334.
41. Conte G., Perdon A.M. The disturbance decoupling problem for systems over a ring. SIAM Journal on Control and Optimization. 33(3):1995;750-764.
42. Conte G., Perdon A.M. Non-interacting control problems for delay-differential systems via systems over rings. JESA, European Journal on Automatic Systems. 31(6):1997;1059-1076.
43. Conte, G., & Perdon, A. M. (1998). Systems over rings: Theory and applications. In First IFAC workshop on linear time delay systems, Grenoble, France, July 1998, Plenary lecture (pp. 223-234).
44. Dambrine, M., Gouaisbaut, F., Perruquetti, W., & Richard, J.-P. (1998). Robustness of sliding mode control under delays effects: A case study. In CESA'98 (IEEE-IMACS conference on computer engineering in system applications), Vol. 1, Tunisia, April 1998 (pp. 817-821).
45. Dambrine M., Richard J.P., Borne P. Feedback control of time-delay systems with bounded control and state. Mathematical Problems in Engineering. 1:1995;77-87.
46. Darouach M. Linear functional observers for systems with delays in state variables. IEEE Transactions on Automatic Control. 46(3):2001;491-496.
47. Darouach M., Pierrot P., Richard E. Design of reduced-order observers without internal delays. IEEE Transactions on Automatic Control. 44(9):1999;1711-1713.
48. Datko R. A paradigm of ill-posedness with respect to time delays. IEEE Transactions on Automatic Control. 43(7):1998;964-967.
49. De Santis A., Germani A., Jetto L. Approximation of the algebraic Riccati equation in the Hilbert space of Hilbert-Schmidt operators. SIAM Journal on Control and Optimization. 4:1993;847-874.
50. Delfour M., Mitter S. Controllability, observability and optimal feedback control of affine, hereditary, differential systems. SIAM Journal on Control and Optimization. 10:1972;298-328.
51. ∞ filtering for uncertain linear systems with multiple time-varying state delays: An LMI approach. In 38th IEEE CDC'99 (Conference on decision and control), Phoenix, AZ, December 1999 (pp. 2023-2028).
52. Dieulot, J. Y., & Richard, J. P. (2001). Tracking control of a nonlinear system with input-dependent delay. In 40th IEEE CDC'01 (Conference on decision and control), Orlando, FL, December 2001.
53. Dion, J. M., Dugard, L., & Niculescu, S. I. (2001). Time delay systems. Kybernetica, 37(3-4) (special issue).
54. Diop S., Kolmanovsky I., Moraal P., vanNieuwstadt M. Preserving stability/performance when facing an unknown time delay. Control Engineering Practice. 9:2001;1319-1325.
55. Dugard L., Verriest E.I. Stability and control of time-delay systems. Lecture notes in control and information sciences. Vol. 228:1997;Springer, Berlin.
56. Dym H., Georgiou T.T., Smith M.C. Explicit formulas for optimally robust controllers for delay systems. IEEE Transactions on Automatic Control. 40(4):1995;656-669.
57. El-Khazaly R. Variable structure robust control of uncertain time-delay systems. Automatica. 34(3):1998;327-332.
58. Elsgolts L.E., Norkin S.B. Introduction to the theory and application of differential equations with deviating arguments. Mathematics in science and engineering. Vol. 105:1973;Academic Press, New York.
59. Engelborghs K., Dambrine M., Roose D. Limitations of a class of stabilization methods for delay systems. IEEE Transactions on Automatic Control. 46(2):2001;336-339.
60. Fairmar F.W., Kumar A. Delay-less observers for systems with delay. IEEE Transactions on Automatic Control. 31(3):1986;258-259.
61. Fattouh, A., Sename, O., & Dion, J. M. (2000). A LMI approach to robust observer design for linear time-delay systems. In 39th IEEE CDC'00 (Conference on decision and control), Sydney, Australia, December 2000.
62. Fiagbedzi Y.A., Pearson A.E. Feedback stabilization of linear autonomous time lag systems. IEEE Transactions on Automatic Control. 31:1986;847-855.
63. Fliess, M., Marquez, R., & Mounier, H. (2001). PID-like regulators for a class of linear delay systems. In ECC'01 (Sixth European control conference), Porto, Portugal, September 2001.
64. Fliess, M., & Mounier, H. (1995). Interpretation and comparison of various types of delay system controllabilities. In IFAC conference on system structure and control, Nantes, France (pp. 330-335).
65. Foda S.G., Mahmoud M.S. Adaptive stabilization of delay differential systems with unknown uncertainty bounds. International Journal on Control. 71(2):1998;259-275.
66. Foias C., Özbay H., Tannenbaum A. Robust control of infinite dimensional systems: A frequency domain method. Lecture notes in control and information sciences. Vol. 209:1996;Springer, Berlin.
67. Fridman E. New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems. System and Control Letters. 43(4):2001;309-319.
68. Fridman E., Fridman L.M., Shustin E.I. Steady modes in a discontinuous control system with time delay and periodic disturbances. ASME Journal of Dynamic Systems, Measurements and Control. 122(4):2000;732-737.
69. ∞ control of linear time-delay systems IEEE Transactions on Automatic Control. 47(2):2002;253-270.
70. Fridman, E., & Shaked, U. (2003). Delay systems. International Journal of Robust and Nonlinear Control, 13(9) (special issue).
71. Fridman, L. M., Fridman, E., & Shustin, E. I. (1996). Steady modes and sliding modes in the relay control systems with time delay. In 35th IEEE CDC'96 (Conference on decision and control), Kobe, Japan (pp. 4601-4606).
72. Fu, M., Li, H., & Niculescu, S. I. (1997). Robust stability and stabilization of time-delay systems via integral quadratic constraint approach. Lecture notes in control and information sciences, Vol. 228. London: Springer (pp. 101-116).
73. ∞ control of uncertain linear jump systems with time-delays Automatica. 37:2001;1141-1146.
74. ∞ state feedback control for linear systems with state delay and parameter uncertainty Automatica. 32(8):1996;1183-1185.
75. Georgiou T.T., Smith M.C. Robust stabilization in the gap metric. Controller design for distributed plants IEEE Transactions on Automatic Control. 37:1992;1133-1143.
76. Georgiou T.T., Smith M.C. Robustness analysis of nonlinear feedback systems. An input-output approach IEEE Transactions on Automatic Control. 42(9):1997;1200-1221.
77. 1 -optimal controllers for delay systems using a two-parameter compensator scheme IEEE Transactions on Automatic Control. 44(8):1999;1512-1521.
78. Germani, A., Manes, C., & Pepe, P. (1996). Linearization of input-output mapping for nonlinear delay systems via static state feedback. In CESA'96 (IEEE-IMACS conference on computer engineering in system applications), Vol. 1, Lille, France (pp. 599-602).
79. Germani, A., Manes, C., & Pepe, P. (1998). A state observer for nonlinear delay systems. In 37th IEEE CDC'98 (Conference on decision and control), Tampa, FL, December 1998 (pp. 355-360).
80. Gibson J.S. Linear quadratic optimal control of hereditary differential systems. Infinite-dimensional Riccati equations and numerical approximation SIAM Journal on Control and Optimization. 31:1983;95-139.
81. Glader C., Hognas G., Mäkilä P.M., Toivonen H.T. Approximation of delay systems. A case study International Journal of Control. 53(2):1991;369-390.
82. Glielmo, L., Santini, S., & Cascella, I. (2000). Stability of linear time-delay systems: A delay-dependent criterion with a tight conservatism bound. In ACC'00 (American control conference), Chicago, IL, June 2000 (pp. 45-49).
83. Glover K., Lam J., Partington J.R. Rational approximation of a class of infinite dimensional system I. Singular value of Hankel operator Mathematics of Control Circulation and Systems. 3:1990;325-344.
84. Glover, K., & Partington, J. R. (1987). Bounds on the achievable accuracy in model reduction (Curtain ed.). Berlin: Springer (pp. 95-118).
85. Glüsing-Lüerßen H. A behavioral approach to delay-differential systems. SIAM Journal on Control and Optimization. 35(2):1997;480-499.
86. Glüsing-Lüerßen, H. (1997b). Realization behaviors given by delay-differential equations. In ECC'97 (Fourth European control conference), Brussels, Belgium, July 1997, pp. WE-M D6.
87. Gorecki H., Fuksa S., Grabowski P., Korytowski A. Analysis and synthesis of time delay systems. 1989;Wiley, New York.
88. Gouaisbaut F., Dambrine M., Richard J.P. Robust control of systems with variable delay. A sliding mode control design via LMIs System and Control Letters. 46(4):2002;219-230.
89. Gouaisbaut, F., Perruquetti, W., Orlov, Y., & Richard, J. P. (1999a). A sliding-mode controller for linear time-delay systems. In ECC'99 (Fifth European control conference), Karlsruhe, Germany.
90. Gouaisbaut, F., Perruquetti, W., & Richard, J. P. (1999b). A sliding-mode control for linear systems with input and state delays. In 38th IEEE CDC'99 (Conference on decision and control), Phoenix, AZ, December 1999 (pp. 4234-4239).
91. Goubet, A., Dambrine, M., & Richard, J. P. (1995). An extension of stability criteria for linear and nonlinear time delay systems. In IFAC conference on system structure and control, Nantes, France (pp. 278-283).
92. Goubet-Bartholomeus A., Dambrine M., Richard J.P. Stability of perturbed systems with time-varying delay. Systems and Control Letters. 31:1997;155-163.
93. Gu K. A generalized discretization scheme of Lyapunov functional in the stability problem of linear uncertain time-delay systems. International Journal on Robust and Nonlinear Control. 9:1999;1-14.
94. Gu G., Khargonekar P.P., Lee E.B. Approximation of infinite-dimensional systems. IEEE Transactions on Automatic Control. 34(6):1992;832-852.
95. Gu K. Discretization schemes for Lyapunov-Krasovskii functionals in time delay systems. Kybernetica. 37(4):2001;479-504.
96. Gu, K., & Niculescu, S. I. (1999). Additional dynamics in transformed time-delay systems. In 38th IEEE CDC'99 (Conference on decision and control), Phoenix, AZ, December 1999 (pp. 4673-4677).
97. Gu K., Niculescu S.I. Further remarks on additional dynamics in various model transformations of linear delay systems. IEEE Transactions on Automatic Control. 46(3):2001;497-500.
98. Hale J.K., Verduyn-Lunel S. Strong stabilization of neutral functional differential equations. IMA Journal of Mathematical Control Information. 19(1-2):2002;5-24.
99. Hale J.K., Verduyn-Lunel S.M. Introduction to functional differential equations. Applied Mathematical Sciences. Vol. 99:1993;Springer, New York.
100. Hennet J.-C., Tarbouriech S. Stability conditions of constrained delay systems via positive invariance. International Journal of Robust and Nonlinear Control. 8(3):1998;265-278.
101. Hirai K., Satoh Y. Stability of a system with variable time-delay. IEEE Transactions on Automatic Control. 25(3):1980;552-554.
102. Hotzel R., Fliess M. On linear systems with a fractional derivation. Introductory theory and examples Mathematics and Computers in Simulation. 45(3-4):1998;385-395.
103. Hsia, T. C., & Gao, L. S. (1990). Robot manipulator control using decentralized time-invariant time-delayed controller. In IEEE international conference on robotics and automation, Cincinnati (pp. 2070-2075).
104. Huang W. Generalization of Lyapunov's theorem in a linear delay system. Journal of Mathematical Analysis and Applications. 142:1989;83-94.
105. Huang Y.P., Zhou K. Robust stability of uncertain time delay systems. IEEE Transactions on Automatic Control. 45(11):2000;2169-2173.
106. Infante E.F., Castelan W.B. A Lyapunov functional for a matrix difference-differential equation. Journal of Differential Equations. 29:1978;439-451.
107. Ionescu V., Niculescu S.I., Dion J.M., Dugard L., Li H. Generalized Popov theory applied to state-delayed systems. Automatica. 37(1):2001;91-97.
108. Ionescu V., Oara C., Weiss M. Generalized Riccati theory. 1998;Wiley, New York.
109. Ivanov, A. F., & Losson, J. (1995). Stable rapidly oscillating solutions in delay equations with negative feedback. Preprint CRM-2292, Center Research Mathematics, University of Montréal (25p).
110. Izmailov R. Analysis and optimization of feedback control algorithms for data transfers in high-speed networks. SIAM Journal of Control and Optimization. 34:1996;1767-1780.
111. Jalili, N., & Olgac, N. (1998). Optimum delayed feedback vibration absorber for MDOF mechanical structure. In 37th IEEE CDC'98 (Conference on decision and control), Tampa, FL, December 1998 (pp. 4734-4739).
112. Jankovic M. Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems. IEEE Transactions on Automatic Control. 46(7):2001;1048-1060.
113. Jeong H.S., Lee C.W. Time delay control with state feedback for azimuth motion of the frictionless positioning device. IEEE-ASME Transactions on Mechatronics. 2(3):1997;161-168.
114. Jun, M., & Safonov, M. G. (2000). Stability analysis of a system with time-delayed states. In ACC'00 (American control conference), Chicago, IL (pp. 949-952).
115. Karrakchou, J., & Rabah, R. (1996). Quelques éléments sur la controlabilité des systèmes en dimension infinie. In CNRS conf. analyse et commande des systèmes avec retards, Nantes, France, March 1996 (pp. 61-78) (in French).
116. Kato J. On Liapunov-Razumikhin type theorems for functional differential equations. The Mathematical Society of Japan, Kobe, Funkcialaj Ekvacioj. 16(3):1973;225-239.
117. Katz, I. I. (1998). Liapunov Method in Stability of Stochastic Systems. Ural Academy of Railway, Ekaterinburg.
118. Khan B.Z., Lehman B. Setpoint PI controllers for systems with large normalized dead time. IEEE Transactions on Control Systems Technology. 4(4):1996;459-466.
119. Kharitonov, V. (1998). Robust stability analysis of time delay systems: A survey. In Fourth IFAC conference on system structure and control, Nantes, France, 8-10 July 1998, Penary lecture (pp. 1-12).
120. Kharitonov V.L., Melchior-Aguliar D. On delay-dependent stability conditions. System and Control Letters. 40(1):2000;71-76.
121. Kharitonov, V. L., & Zhabko, A. P. (2001). Lyapunov-Krasovski approach to robust stability of time delay systems. In First IFAC/IEEE symposium on system structure and control, Prague, Technical report, August 2001.
122. Kim W.S., Hannaford B., Bejczy A.K. Force-reflection and shared compliant control in operating telemanipulators with time-delay. IEEE Transactions on Robotics and Automation. 8(2):1992;176-185.
123. Kojima A., Uchida K., Shimemura E., Ishijima S. Robust stabilization of a system with delays in control. IEEE Transactions on Automatic Control. 39(8):1994;1694-1698.
124. Kolmanovskii V.B. Stability of some nonlinear functional differential equations. Journal of Nonlinear Differential Equations. 2:1995;185-198.
125. Kolmanovskii V.B., Maizenberg T.L., Richard J.P. Mean square stability of difference equations with a stochastic delay. Nonlinear Analysis. 52(3):2003;795-804.
126. Kolmanovskii V.B., Myshkis A. Applied theory of functional differential equations. Mathematics and Applications. Vol. 85:1992;Kluwer Academy, Dordrecht.
127. Kolmanovskii V.B., Myshkis A. Introduction to the theory and applications of functional differential equations. 1999;Kluwer Academy, Dordrecht.
128. Kolmanovskii, V. B., Niculescu, S. I., & Gu, K. (1999a). Delay effects on stability: A survey. In 38th IEEE CDC'99 (Conference on decision and control), Phoenix, AZ, December 1999 (pp. 1993-1998).
129. Kolmanovskii V.B., Niculescu S.I., Richard J.P. On the Liapunov-Krasovskii functionals for stability analysis of linear delay systems. International Journal on Control. 72(4):1999;374-384.
130. Kolmanovskii V.B., Nosov V.R. Stability of functional differential equations. 1986;Academic Press, London.
131. Kolmanovskii V.B., Richard J.P. Stability of some linear systems with delay. IEEE Transactions on Automatic Control. 44(5):1999;984-989.
132. Kolmanovskii V.B., Shaikhet L.E. Control of systems with aftereffect. Transaction of Mathematical monographs. Vol. 157:1996;American Mathematical Society, Providence, RI.
133. Kolmanovskii, V. B., Tchangani, P. A., & Richard, J. P. (1998). Stability of linear systems with discrete-plus-distributed delay: Application of some model transformations. In MTNS'98 (13th symposium on mathematical theory of networks and systems), Padova, Italy, July 1998.
134. Krasovskii, N. N. (1963). Stability of motion. Stanford University Press, Stanford CA, USA, (translation by J. Brenner).
135. Krtolica R., Özguner Ü., Chan H., Göktas H., Winkelman J., Liubakka M. Stability of linear feedback systems with random communication delays. International Journal of Control. 59(4):1991;925-953.
136. Kwon H.W., Pearson A.E. Feedback stabilization of linear systems with delayed control. IEEE Transactions on Automatic Control. 25(2):1980;266-269.
137. Lafay, J. F., Fliess, M., Mounier, H., & Sename, O. (1996). Sur la commandabilité des systèmes linéaires à retards. In CNRS conference analysis and control of systems with delays, Nantes, France, 1996 (pp. 19-42) (in French).
138. Lakshmikantham, V., & Leela, S. (1969). Differential and integral inequalities, Vol. 2. New York: Academic Press.
139. ∞ controller for state and input delayed systems with structured uncertainties. In 35th IEEE CDC'96 (Conference on decision and control), Kobe, Japan (pp. 2092-2096).
140. Lehman B. The influence of delays when averaging slow and fast oscillating systems. Overview IMA Journal of Mathematical Control Information. 19(1-2):2002;201-216.
141. Lehman, B., & Weibel, S. P. (1998). Averaging theory for functional differential equations. In 37th IEEE CDC'98 (Conference on decision and control), Tampa, FL, December 1998 (pp. 1352-1357).
142. Lelevé, A., Fraisse, P., & Dauchez, P. (2001). Telerobotics over IP networks: Towards a low level real time architecture. In IROS'01 (International conference on intelligent robots and systems), Maui, Hawaii, October 2001.
143. Lewis R.M. Control-delayed system properties via an ordinary model. International Journal of Control. 30(3):1979;477-490.
144. Leyva-Ramos J., Pearson A.E. An asymptotic modal observer for linear autonomous time lag systems. IEEE Transactions on Automatic Control. 40:1995;1291-1294.
145. ∞ control of uncertain linear time-delay systems. In Proceedings of 13th IFAC world congress, San Francisco, CA, Vol. H (pp. 113-118).
146. Loiseau, J. J. (1994). A 2-D transfert without minimal realization. In Sprann'94, IMACS, Lille, France (pp. 97-100).
147. Loiseau, J. J. (1998). Algebraic tools for the control and stabilization of time-delay systems. In First IFAC workshop on linear time delay systems, Grenoble, France, July 1998, Plenary lecture (pp. 234-249).
148. Loiseau J.J. Invariant factors assignment for a class of time-delay systems. Kybernetika. 37(3):2001;265-276.
149. Loiseau J.J., Brethé D. 2-D exact model matching with stability, the structural approach. Bulletin of the Polish Academy of Science - Technical Sciences. 45(2):1997;309-317.
150. Loiseau J.J., Brethé D. The use of 2-D systems theory for the control of time-delay systems. JESA, European Journal of Automatic Systems. 31(6):1997;1043-1058.
151. Loiseau J.J., Brethé D. An effective algorithm for finite spectrum assignment of single-input systems with delays. Mathematics and Computers in Simulation. 45(3-4):1998;339-348.
152. Loiseau, J. J., & Rabah, R. (1997). Analysis and control of time-delay systems. JESA. European Journal of Automatic Systems, 31(6) (Special issue of JESA).
153. Louisell, J. (1991). A stability analysis for a class of differential-delay equations having time-varying delay. Lecture Notes in Mathematics, Vol. 1475 (Busenberg and Martelli ed.), chapter Delay differential equations and dynamical systems (pp. 225-242). Berlin: Springer.
154. Louisell J. Delay differential systems with time-varying delay. New directions for stability theory Kybernetika. 37(3):2001;239-252.
155. Luck R., Ray A. An observer-based compensator for distributed delays. Automatica. 26(5):1990;903-908.
156. Luo, N., & De la Sen, M. (1992). State feedback sliding mode controls of a class of time-delay systems. In ACC'92 (American control conference), Chicago, IL (pp. 894-895).
157. Luo N., De la Sen M. State feedback sliding mode control of a class of uncertain time-delay systems. IEE Proceedings-D. 140(4):1993;261-274.
158. MacDonald N. Biological delay systems: Linear stability theory. Cambridge Studies in Mathematics Biology. Vol. 8:1989;Cambridge University Press, Cambridge.
159. Mahmoud, M. S. (2000). Robust control and filtering for time-delay systems. Control Engineering Series. New York: Marcel Dekker.
160. Majhi, S., & Atherton, D. (1998). A new Smith predictor and controller for unstable and integrating processes with time delay. In 37th IEEE CDC'98 (Conference on decision and control), Tampa, FL, December 1998 (pp. 1341-1345).
161. Majhi, S., & Atherton, D. P. (1999). A novel identifcation method for time delay processes. In ECC'99 (Fifth European control conference), Karslruhe, Germany.
162. Mäkilä P.M., Partington J.R. Laguerre and Kautz shift approximations of delay systems. International Journal of Control. 72:1999;932-946.
163. Mäkilä P.M., Partington J.R. Shift operator induced approximations of delay systems. SIAM Journal of Control and Optimization. 37(6):1999;1897-1912.
164. Manitius A., Olbrot A.W. Finite spectrum assignment problem for systems with delays. IEEE Transactions on Automatic Control. 24(4):1979;541-553.
165. Mascolo S. Congestion control in high speed communication networks using the Smith principle. Automatica. 35:1999;1921-1935.
166. Mazenc, F., Mondié, S., & Niculescu, S. I. (2001). Global asymptotic stabilization for chains of integrators with a delay in the input. In 40th IEEE CDC'01 (Conference on decision and control), Orlando, FL, December 2001.
167. Megretski A., Rantzer A. System analysis via integral quadratic constraints. IEEE Transactions on Automatic Control. 42(6):1997;819-830.
168. ∞ control for dead-time systems IEEE Transactions on Automatic Control. 45(2):2000;272-285.
169. Mérigot, A., & Mounier, H. (2000). Quality of service and MPEG4 video transmission. In MTNS'00 (14th symposium on mathematical theory of networks and systems), Perpignan, France.
170. Mirkin, L. (2000). On the extraction of dead-time controllers from delay-free parametrizations. In Second IFAC workshop on linear time delay systems, Ancona, Italy, September 2000 (pp. 157-162).
171. ∞ control of systems with I/O delay A review of some problem-oriented methods IMA Journal of Mathematical Control and Information. 19(1-2):2002;185-200.
172. Mondié, S., Niculescu, S. I., & Loiseau, J. J. (2001). Delay robustness of closed loop finite assignment for input delay systems. In Third IFAC workshop on time delay systems, Sante Fe, NM, December 2001 (pp. 233-238).
173. e IEEE conf. internat. francophone d'Automatique, Lille, France, July 2000 (pp. 201-206).
174. Moog C.H., Castro-Linares R., Velasco-Villa M., Marquez-Martinez L.A. The disturbance decoupling problem for time-delay nonlinear systems. IEEE Transactions on Automatic Control. 45(2):2000;305-309.
175. Mounier, H., Mboup, M., Petit, N., Rouchon, P., & Seret, D. (1998). High speed network congestion control with a simplified time-varying delay model. In IFAC conference on system, structure, control, Nantes, France.
176. Mounier H., Rouchon P., Rudolph J. Some examples of linear systems with delays. JESA, European Journal of Automatic Systems. 31(6):1997;911-926.
177. Mounier H., Rudolph J. Flatness based control of nonlinear delay systems. A chemical reactor example International Journal of Control. 71:1998;871-890.
178. ∞ control and estimation problems with delayed measurements State space solutions SIAM Journal on Control and Optimization. 35(4):1997;1217-1243.
179. ∞ control of a class of nonlinear systems with delayed state and control: A LMI approach. In 37th IEEE CDC'98 (Conference on decision and control), Tampa, FL, December 1998 (pp. 2384-2389).
180. Nguang S.K. Comments on "Robust stabilization of uncertain input-delay systems by SMC with delay compensation" Automatica. 37:2001;1677.
181. ∞ memoryless control with an α -stability constraint for time delays systems An LMI approach IEEE Transactions on Automatic Control. 43(5):1998;739-743.
182. Niculescu S.I. Delay effects on stability. Lecture notes in control and information sciences. Vol. 269:2001;Springer, Berlin.
183. Niculescu, S. I., & Chen, J. (1999). Frequency sweeping tests for asymptotic stability: A model transformation for multiple delays. In 38th IEEE CDC'99 (Conference on decision and control), Phoenix, USA, December 1999 (pp. 4678-4683).
184. Niculescu S.I., De Souza C.E., Dugard L., Dion J.M. Robust exponential stability of uncertain systems with time-varying delays. IEEE Transactions on Automatic Control. 43(5):1998;743-748.
185. Niculescu S.I., Dion J.M., Dugard L. Robust stabilization for uncertain time-delay systems containing saturating actuators. IEEE Transactions on Automatic Control. 41(5):1996;742-747.
186. Niculescu S.I., Lozano R. On the passivity of linear delay systems. IEEE Transactions on Automatic Control. 46(3):2001;460-464.
187. Niculescu S.I., Richard J.P. Analysis and design of delay and propagation systems. IMA Journal of Mathematical Control and Information. 19(1-2):2002;1-227. (special issue).
188. Niculescu, S. I., Verriest, E. I., Dugard, L., & Dion, J. M. (1997). Stability and robust stability of time-delay systems: A guided tour. Lecture notes in control and information sciences, Vol. 228 (pp. 1-71). London: Springer.
189. Niemeyer, G. (1996). Using wave variables intime delayed force reflecting teleoperation. Ph.D. thesis, MIT, Cambridge, MA.
190. Niemeyer, G., & Slotine, J. J. (1998). Towards force-reflecting teleoperation over the internet. In IEEE international conference on robotics and automation, Leuven, Belgium, May 1998 (pp. 1909-1915).
191. Nilsson, J. (1998). Real-time control systems with delays. Ph.D. thesis, Department of Automatic Control, Lund Institute of Technology, Lund, Sweden.
192. Nilsson J., Bernhardsson B., Wittenmark B. Stochastic analysis and control of real-time systems with random delays. Automatica. 34(1):1998;57-64.
193. Oguchi, T., Watanabe, A., & Nakamizo, T. (1998). Input-output linearization of retarded nonlinear systems by an extended Lie derivative. In 37th IEEE CDC'98 (Conference on decision and control), Tampa, FL, December 1998 (pp. 1364-1369).
194. Ohta Y., Kojima A. Formulas for Hankel singular values and vectors for a class of input delay systems. Automatica. 35:1999;201-215.
195. Olbrot A.W. Algebraic criteria of controllability to zero function for linear constant time-lag systems. Control and Cybernetics. 2(1/2):1973;59-77.
196. Olbrot A.W. A sufficiently large time delay in feedback loop must destroy exponential stability of any decay rate. IEEE Transactions on Automatic Control. 29:1984;367-368.
197. Olbrot, A. W. (1998). Finite spectrum property and predictors. In First IFAC workshop on linear time delay systems, Grenoble, France, July 1998, Plenary lecture (pp. 251-260).
198. Orlov Y., Belkoura L., Dambrine M., Richard J.P. On identifiability of linear time-delay systems. IEEE Transactions on Automatic Control. 47(8):2002;1319-1324.
199. Orlov, Y., Belkoura, L., Richard, J. P., & Dambrine, M. (2003). Adaptive identification of linear time-delay systems. International Journal on Robust and Nonlinear Control, 13(9), 857-872 (Special issue on TDS E. Fridman and U. Shaked).
200. Orlov Y.V. Optimal delay control - Part I. Automation and Remote Control. 49(12):1988;1591-1596. (Transl. from Avtomatika i Telemekhnika, No. 12, 1988).
201. Orlov Y.V. Optimal delay control - Part I. Automation and Remote Control. 49(12):1988;1591-1596. (Transl. from Avtomatika i Telemekhnika, No. 12, 1988).
202. Orlov Y.V. Discontinuous unit feedback control of uncertain infinite-dimensional systems. IEEE Transactions on Automatic Control. 45(5):2000;834-843.
203. Orlov Y.V., Utkin V.I. Sliding mode control in infinite-dimensional systems. Automatica. 6:1987;753-757.
204. Oucheriah S. Robust tracking and model following of uncertain dynamic delay. IEEE Transactions on Automatic Control. 44(7):1999;1473-1477.
205. Palmor, Z. J. (1996). Time-delay compensation - Smith predictor and its modifications. In W.S. Levine (Ed.), The control handbook (pp. 224-237). CRSC PressPress, Boca Raton, FL, USA.
206. Partington J.R. Approximation of unstable infinite-dimensional systems using coprime factors. System and Control Letters. 16(2):1991;89-96.
207. Pepe, P. (1996). Il controllo LQG dei sistemi con ritardo. Department of Electrical Engineering and Univiversity l'Aquila, Italy (in Italian).
208. Perruquetti W., Barbot J.P. Sliding mode control for engineers. Control Engineering Series. Vol. 11:2002;Marcel Dekker, New York.
209. Petit, N. (2000). Systèmes à Retards. Platitude en Génie des Procédés et Contrôle de Certaines Équations des Ondes. Ecole des Mines de Paris (in French).
210. Picard, P., & Lafay, J. F. (1995). Further results on controllability of linear systems with delay. In ECC'95 (Third European control conference, Rome) (pp. 3313-3318).
211. Picard P., LaFay J.F., Kucera V. Feedback realization of nonsingular precompensators for linear systems with delays. IEEE Transactions on Automatic Control. 42(6):1997;848-852.
212. Picard P., Lafay J.F., Kucera V. Model matching for linear systems with delays and 2-D systems. Automatica. 35(3):1998;183-191.
213. Picard, P., Sename, O., & Lafay, J. F. (1996). Observers and observability indices for linear systems with delays. In CESA'96 (IEEE-IMACS conference on computer engineering in system applications), Lille, France, Vol. 1, July 1996 (pp. 81-86).
214. ∞ controller design for congestion control in communication networks with a capacity predictor. In 40th IEEE CDC'01 (Conference on decision and control), Orlando, FL, December 2001 (pp. 598-603).
215. Rabah R., Malabre M. On the structure at infinity of linear delay systems with application to the disturbance decoupling problem. Kybernetica. 35:1999;668-680.
216. Ray A. Output feedback control under randomly varying distributed delays. Journal of Guidance, Control and Dynamics. 17(4):1994;701-711.
217. Razumikin B.S. On the stability of systems with a delay. Prikladnava Matematika i Mekhanika. 20:1956;500-512. (in Russian).
218. Rekasius, Z. V. (1980). A stability test for systems with delays. In Proceedings on joint automatic control conference. San Francisco, CA (pp. TP9-A).
219. Richard, J. P. (1998). Some trends and tools for the study of time delay systems. In Second conference IMACS-IEEE CESA'98, computational engineering in systems applications, Tunisia, April 1998, Plenary lecture (pp. 27-43).
220. Richard, J. P. (2000). Linear time delay systems: Some recent advances and open problems. In Second IFAC workshop on linear time delay systems. Ancona, Italy, September 2000, Plenary lecture.
221. Richard J.P., Gouaisbaut F., Perruquetti W. Sliding mode control in the presence of delay. Kybernetica. 37(4):2001;277-294.
222. Richard, J. P., Goubet, A., Tchangani, P. A., & Dambrine, M. (1997). Nonlinear delay systems: Tools for a quantitative approach to stabilization. Lecture notes in control and information sciences, Vol. 228 (pp. 218-240). London: Springer.
223. Richard, J. P., & Kolmanovskii, V. (1998). Special Issue on Delay systems. Mathematics and Computers in Simulation, 45 (3-4).
224. Roh Y.H., Oh J.H. Robust stabilization of uncertain input-delay systems by sliding mode control with delay compensation. Automatica. 35:1999;1681-1685.
225. Rudolph, J., & Mounier, H. (2000). Trajectory tracking for π-flat nonlinear delay systems with a motor example. Lecture notes in control and information sciences, Vol. 258 (Respondek ed.) (pp. 339-352). London, Isidori, Lamnabhi, Laguarrigue: Springer.
226. Safonov M.G. Stability and robustness of multivariable feedback systems. 1980;MIT Press, Cambridge, MA.
227. Sename, O. (1994). Sur la commandabilité et le découplage des systèmes linéaires à retards. Laboratoire d'Automatique de Nantes, University of Nantes and EC Nantes, France (in French).
228. Sename O. New trends in design of observers for time-delay systems. Kybernetica. 37(4):2001;427-458.
229. Shakkottai, S., Srikant, R. T., & Meyn, S. (2001). Boundedness of utility function based congestion controllers in the presence of delay. In 40th IEEE CDC'01 (Conference on decision and control), Orlando, FL, December 2001 (pp. 616-621).
230. Shin K.G., Cui X. Computing time delay and its effects on real-time control systems. IEEE Transactions on Control and System Technology. 3(2):1995;218-224.
231. Shyu K.K., Yan J.J. Robust stability of uncertain time-delay systems and its stabilization by variable structure control. International Journal of Control. 57:1993;237-246.
232. Silva, G. J., Datta, A., & Bhattacharyya, S. P. (2001). Controller design via Padé approximation can lead to instability. In 40th IEEE CDC'01 (Conference on decision and control), Orlando, FL, December 2001 (pp. 4733-4737).
233. Sira-Ramirez, H., & Angulo-Nunez, M. I. (1998). On the passivity based regulation of a class of delay differential systems. In 37th IEEE CDC'98 (Conference on decision and control), Tampa, FL, December 1998 (pp. 297-298).
234. Slater G.L., Wells W.R. On the reduction of optimal time delay systems to ordinary ones. IEEE Transactions on Automatic Control. 17:1972;154-155.
235. Smith O.J.M. A controller to overcome dead time. ISA Journal of Instrument Society of America. 6:1959;28-33.
236. Smith, O. J. M. (1957). Posicast control of damped oscillatory systems. In Proceedings of the IRE, Vol. 45 (pp. 1249-1255).
237. Sontag E.D. The lattice of minimal realizations of response maps over rings. Mathematical Systems Theory. 11:1977;169-175.
238. ∞ problem in systems with a single input delay IEEE Transactions on Automatic Control. 45(3):2000;382-397.
239. Tan K.K., Wang Q.K., Lee T.H. Finite spectrum assignment control of unstable time delay processes with relay tuning. Industrial Engineering and Chemical Research. 37(4):1998;1351-1357.
240. Tarbouriech S., Gomes Da Silva J.M. Synthesis of controllers for continuous time delay systems with saturating controls via LMIs. IEEE Transactions on Automatic Control. 45(1):2000;105-111.
241. Teel A.R. Connection between Razumikhin-type theorems and the ISS nonlinear small gain theorem. IEEE Transactions on Automatic Control. 43(7):1998;960-964.
242. Thowsen A. An analytical stability test for a class of linear time-delay systems. IEEE Transactions on Automatic Control. 25:1981;735-736.
243. Tits A.L., Balakrishnan V. Small-μ theorem with frequency-dependent uncertainty bounds Mathematics of Control Signals and Systems. 11(3):1998;220-243.
244. Tsoi, A. C. (1978). Recent advances in the algebraic system theory of delay differential equations. Recent theoretical developments in control (Gregson ed.) (pp. 67-127). New York: Academic Press.
245. Tsypkin Ya.Z. The systems with delayed feedback. Avtomatika i Telemekhnika. 7:1946;107-129.
246. Tuch J., Feuer A., Palmor Z.J. Time delay estimation in continuous linear time-invariant systems. IEEE Transactions on Automatic Control. 39:1994;823-827.
247. ∞ control for distributed parameter systems: A state space approach:1993;Birkhauser, Basel.
248. VanAssche, V., Dambrine, M., Lafay, J. F., & Richard, J. P. (1999). Some problems arising in the implementation of distributed-delay control laws. In 38th IEEE CDC'99 (Conference on decision and control), Phoenix, AZ, December 1999 (pp. 4668-4672).
249. Verduyn-Lunel, S. M. (1997). Identification problems in functional differential equations. In 36th IEEE CDC'97 (Conference on decision and control), San Diego, CA, December 1997 (pp. 4409-4413).
250. Verriest, E. I. (1999). Robust stability and adaptive control of time-varying neutral systems. In 38th IEEE CDC'99 (Conference on decision and control), Phoenix, AZ, December 1999 (pp. 4690-4695).
251. Verriest E.I. Stability of systems with state-dependent and random delays. IMA Journal on Mathematical Control and Information. 19(1-2):2002;103-114.
252. Verriest E.I., Aggoune W. Stability of nonlinear differential delay systems. Mathematics and Computers in Simulation. 45(3-4):1998;257-268.
253. Walton K., Marshall J.E. Direct method for TDS stability analysis. IEE Proceedings, Part D. 134:1987;101-107.
254. ∞ observer design for uncertain time-delay systems: (I) the continuous case. In IFAC 14th world congress, Beijing, China (pp. 231-236).
255. ∞ observer design of linear state delayed systems with parametric uncertainty The discrete-time case Automatica. 35(6):1999;1161-1167.
256. Wang, Z. Q., & Skogestad, S. (1993). Robust controller design for uncertain time delay systems. Lecture notes in control and information sciences, Vol. 185 (Curtain, Bensoussan and Lions ed.) (pp. 610-622). Berlin: Springer.
257. Wang Q.G., Zhang Y. Robust identification of continuous systems with dead-time from step responses. Automatica. 37:2001;377-390.
258. Watanabe, K., Nobuyama, E., & Kojima, K. (1996). Recent advances in control of time-delay systems a tutorial review. In 35th IEEE CDC'96 (Conference on decision and control), Kobe, Japan, December 1996 (pp. 2083-2089).
259. Weiss L. On the controllability of delay-differential equations. SIAM Journal on Control and Optimization. 5(4):1967;575-587.
260. Willems J. The analysis of feedback systems. 1971;MIT Press, Cambridge, MA.
261. Willems J. Paradigms and puzzles in the theory of dynamical systems. IEEE Transactions on Automatic Control. 36:1991;259-294.
262. Wu F., Grigoriadis K.M. LPV systems with parameter-varying time delays. Analysis and control Automatica. 37:2001;221-229.
263. Yamanaka K., Ushida K., Shimemura E. Optimal control of systems with random delay. International Journal on Control. 29(3):1979;489-495.
264. Yao Y.X., Zhang Y.M., Kovacevic R. Functional observer and state feedback for input time-delay systems. International Journal on Control. 66(4):1997;603-617.
265. Yoon M.G., Lee B.H. A new approximation method for time-delay systems. IEEE Transactions on Automatic Control. 42(7):1997;1008-1012.
266. Youcef-Toumi K., Ito O. A time delay controller design for systems with unknown dynamics. ASME Journal on Dynamic Systems Measurement and Control. 112:1990;133-142.
267. Youcef-Toumi K., Reddy S. Analysis of linear time invariant systems with time delay. ASME Journal on Dynamic Systems Measurement and Control. 114(4):1992;623-633.
268. Youcef-Toumi K., Reddy S. Dynamic analysis anf control of high speed and high precision active magnetic bearings. ASME Journal on Dynamic Systems Measurement and Control. 14(4):1992;544-555.
269. Youcef-Toumi K., Wu S.T. Input-output linearization using time delay control. ASME Journal on Dynamic Systems Measurement and Control. 114:1992;10-19.
270. Zhang, J., Knospe, C. R., & Tsiotras, P. (2000). Stability of linear time-delay systems: A delay-dependent criterion with a tight conservatism bound. In ACC'00 (American control conference), Chicago, IL, June 2000 (pp. 1458-1462).
271. Zheng F., Cheng M., Gao W.B. Variable structure control of TDS with a simulation study on stabilizing combustion in liquid propellant rocket motors. Automatica. 31(7):1995;1031-1037.
272. Zhou K., Khargonekar P.P. On the weighted sensitivity minimization problem for delay systems. System and Control Letters. 8:1987;307-312.