Stability analysis of systems with uncertain time-varying delays

Automatica

Volumn 43, Issue 6, 2007, Pages 959-970

  Kao, Chung Yao ^a   Rantzer, Anders ^b  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b LUND UNIVERSITY   (Sweden)

Author keywords

Integral quadratic constraint; Robust stability analysis; Time varying delay

Indexed keywords

LINEAR MATRIX INEQUALITIES; PARAMETER ESTIMATION; PROBLEM SOLVING; ROBUST CONTROL; STABILITY; TIME VARYING NETWORKS;

INTEGRAL QUADRATIC CONSTRAINTS; ROBUST STABILITY ANALYSIS; TIME-VARYING DELAY;

UNCERTAIN SYSTEMS;

EID: 34247521318     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2006.12.006     Document Type: Article

References (38)

1. Cao Y., Sun Y., and Cheng C. Delay-dependent robust stabilization of uncertain systems with multiple delay. IEEE Transactions on Automatic Control 43 11 (1998) 1608-1612
2. Cervin A., Henriksson D., Lincoln B., and Årzén K. Analysis of control performance in real-time systems. IEEE Transactions on Automatic Control 23 3 (2003) 16-30
3. Chen J., and Latchman H.A. Frequency sweeping tests for stability independent of delay. IEEE Transactions on Automatic Control 40 9 (1995) 1640-1645
4. Cho, D., & Hedrick, J. K. (1989). Automative powertrain modelling for control. ASME Transaction, 568-576.
5. Fridman E., and Shaked U. An improved stabilization method for linear time-delay systems. IEEE Transactions on Automatic Control 47 11 (2002) 1931-1937
6. ∞ control: Constant and time-varying delays. International Journal of Control 76 1 (2003) 48-60
7. 2-gain analysis of systems with time-varying delays: Input-output approach. In Proceedings of the 44th IEEE conference on decision and control and the European control conference 2005. Seville, Spain.
8. Fu, M., Li, H., & Niculescu, S. I. (1998). Robust stability and stabilization of time-delay systems via integral quadratic constraint approach. In L. Dugard, E. I. Verriest (Eds.), Stability and control of time-delay systems (Vol. 228, pp. 101-115). Berlin: Springer.
9. Gu, K., & Han, Q.-L. (2000). Discretized Lyapunov functional for linear uncertain systems with time-varying delay. In Proceedings of the American control conference.
10. Gu K., Kharitonov V.L., and Chen J. Stability of time-delay systems (2003), Birkhäuser, Boston
11. Gu K., and Niculescu S.-I. Additional dynamics in transformed time-delay systems. IEEE Transactions on Automatic Control 45 3 (2000) 572-575
12. Han Q.-L., and Gu K. On robust stability of time-delay systems with norm-bounded uncertainty. IEEE Transactions on Automatic Control 46 9 (2001) 1426-1431
13. Huang Y., and Zhou K. Robust stability of uncertain time-delay systems. IEEE Transactions on Automatic Control 45 11 (2000) 2169-2173
14. Jun M., and Safonov M.G. Iqc analysis for time-delay systems. International Journal of Robust and Nonlinear Control 11 (2001) 1455-1468
15. Jun M., and Safonov M.G. Rational multiplier iqcs for uncertain time-delays and LMI stability conditions. IEEE Transactions on Automatic Control 47 11 (2002) 1871-1875
16. Kao C.-Y., and Lincoln B. Simple stability criteria for systems with time-varying delays. Automatica 40 8 (2004) 1429-1434
17. Kao, C.-Y., Megretski, A., Jönsson, U., & Rantzer, A. (2004). A MATLAB toolbox for robustness analysis. In Proceedings of the 2004 IEEE conference on computer aided control systems design. Taipei, Taiwan.
18. Kao, C.-Y., & Rantzer, A. (2005). Robust stability analysis of linear systems with time-varying delays. In Proceedings of the 16th IFAC world congress. Prague, Czech Republic.
19. Kharitonov V.L., and Niculescu S.-I. On the stability of linear systems with uncertain delay. IEEE Transactions on Automatic Control 48 1 (2003) 127-132
20. Kim J.-H. Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty. IEEE Transactions on Automatic Control 46 5 (2001) 789-792
21. Kolmanovskii, V. B., Niculescu, S.-I., & Gu, K. (1999). Delay effects on stability: A survey. In Proceedings of the 38th IEEE conference on decision and control.
22. Kolmanovskii V.B., and Richard J.-P. Stability of some linear systems with delays. IEEE Transactions on Automatic Control 44 5 (1999) 984-989
23. Li X., and de Souza C.E. Criteria for robust stability and stabilization of uncertain linear systems with state delay. Automatica 33 9 (1997) 1657-1662
24. Li X., and de Souza C.E. Delay-dependent robust stability and stabilization of uncertain linear delay systems: A linear matrix inequality approach. IEEE Transactions on Automatic Control 42 8 (1997) 1144-1148
25. Low S.H., Paganini F., and Doyle J. Internet congestion control. IEEE Control Systems Magazine 22 1 (2002) 28-43
26. Megretski A., and Rantzer A. System analysis via integral quadratic constraints. IEEE Transactions on Automatic Control 42 6 (1997) 819-830
27. Mehdi D., Boukas E.K., and Liu Z.-K. Dynamical systems with multiple time-varying delays: Stability and stabilizability. Journal of Optimization Theory and Applications 113 3 (2002) 537-565
28. Misra, V., Gong, W. B., & Towsley, D. (2002). Fluid-based analysis of a network of AQM routers supporting TCP-flows with an application to RED. In Proceedings of ACM/SIGCOMM.
29. Morari M., and Zafirious E. Robust process control (1989), Prentice-Hall, Englewood Cliffs, NJ
30. Niculescu, S.-I. (2001). Delay effects on stability. A robust control approach. Lecture notes in control and information sciences. Heidelberg: Springer.
31. Park P. A delay-dependent stability criterion for systems with uncertain time-invariant delays. IEEE Transactions on Automatic Control 44 4 (1999) 876-877
32. ∞ control of linear uncertain time-delay systems-a projection approach. IEEE Transactions on Automatic Control 51 4 (2006) 680-685
33. Wang Z.Q., Lundström P., and Skogestad S. Representation of uncertain time delays in the H-infinity framework. International Journal of Control 59 3 (1994) 627-638
34. Wu M., He Y., She J.-H., and Liu G.-P. Delay-dependent criteria for robust stability of time-varying delay systems. Automatica 40 8 (2004) 1435-1439
35. Xu S., and Lam J. Improved delay-dependent stability criteria for time-delay systems. IEEE Transactions on Automatic Control 50 3 (2005) 384-387
36. Zhang J., Knope C.R., and Tsiotras P. Stability of time-delay systems: Equivalence between Lyapunov and scaled small-gain conditions. IEEE Transactions on Automatic Control 46 3 (2001) 482-486
37. Zhang J., Knope C.R., and Tsiotras P. New results on delay-dependent control of time-delay systems. IEEE Transactions on Automatic Control 50 1 (2005) 95-100
38. Zhang W., Branicky M.S., and Phillips S.M. Stability of networked control systems. IEEE Control Systems Magazine 21 1 (2001) 84-99