Stability of Retarded Dynamical Systems: A Lyapunov Function Approach

Journal of Mathematical Analysis and Applications

Volumn 253, Issue 2, 2001, Pages 590-615

  Xu, Bugong ^a  

^a SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035863970     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.7167     Document Type: Article

References (50)

1. Krasovskii N. N. Stability of Motion. 1963;Stanford Univ. Press, Stanford.
2. Razumikhin B. S. The application of Lyapunov's method to problems in the stability of systems with delay. Automat. Remote Control. 21:1960;515-520.
3. Qin Y. X., Liu Y. Q., Wang L. Stability of Motion for Dynamic Systems with Time Delay. 1963;Science Press, Beijing.
4. Lakshmikantham V., Leela S. Differential and Integral Inequalities: Theory and Applications. 1969;Academic Press, New York/London.
5. Hale J. K. Theory of Functional Differential Equations. 1977;Springer-Verlag, New York.
6. Hale J. K., Lunel S. M. V. Introduction to Functional Differential Equations. 1993;Springer-Verlag, New York.
7. Kolmanovskii V. B., Nosov V. R. Stability of Functional Differential Equations. 1986;Academic Press, London.
8. Li S. L., Wun L. Z. Functional Differential Equations. 1987;Hunan Science and Technology Press, Changsha.
9. Dugard L., Verriest E. I. Stability and Control of Time-Delay Systems. 1998;Springer-Verlag, London.
10. Kamen E. W. On the relationship between zero criteria for two-variable polynomials and asymptotic stability of delay differential equations. IEEE Trans. Automat. Control. 25:1980;982-983.
11. Kamen E. W. Linear systems with commensurate time delays: Stability and stabilization independent of delay. IEEE Trans. Automat. Control. 27:1982;367-375.
12. Kamen E. W. Correction to "Linear systems with commensurate time delays: Stability and stabilization independent of delay. IEEE Trans. Automat. Control. 28:1983;248-249.
13. Brierley S. D., Chiasson J. N., Lee E. B., Zak S. H. On stability independent of delay for linear systems. IEEE Trans. Automat. Control. 27:1982;252-254.
14. Chiasson J. N., Brierley S. D., Lee E. B. A simplified deviation of the Zeheb-Walach 2-D stability test with applications to time-delay systems. IEEE Trans. Automat. Control. 30:1985;411-414.
15. Mori T. Criteria for asymptotic stability of linear time-delay systems. IEEE Trans. Automat. Control. 30:1985;158-161.
16. Bourles H. α-stability of systems governed by a functional differential equation - Extension of results concerning linear delay systems. Internat. J. Control. 45:1987;2233-2234.
17. Hale J. K., Infante E. F., Tsen F. S. P. Stability in linear delay equations. J. Math. Anal. Appl. 105:1985;533-555.
18. Liao X., Wang X. Stability for differential difference equations. J. Math. Anal. Appl. 173:1993;84-102.
19. J. Chen and H. A. Latchamn, Asymptotic stability independent of delays: Simple necessary and sufficient conditions, inProc. 1994 ACC, Baltimore, MD, 1994, Vol. 1, pp. 1027-1031.
20. Lehman B., Shujaee K. Delay independent stability conditions and decay estimates for time-varying functional differential equations. IEEE Trans. Automat. Control. 39:1994;1673-1676.
21. S. I. Niculescu, A. T. Neto, J. M. Dion, and L. Dugard, Delay-dependent stability of linear systems with delayed state: A LMI approach, inProc. 34th CDC, New Orleans, LA, 1995, Vol. 2, pp. 1495-1496.
22. X. Li and C. E. de Souza, LMI approach to delay-dependent robust stability and stabilization of uncertain linear delay systems, inProc. 34th CDC, New Orleans, LA, 1995, Vol. 4, pp. 3614-3619.
23. Su J. H. Further results on the robust stability of linear systems with a single delay. Systems Control Lett. 23:1995;375-379.
24. Trinh H., Aldeen M. Stability robustness bounds for linear systems with delayed perturbation. IEE Proc. Control Theory Appl. 142:1995;345-350.
25. Wu H., Mizukami K. Robust stability criteria for dynamical systems including delayed perturbations. IEEE Trans. Automat. Control. 40:1995;487-490.
26. Chen J., Xu D., Shafai B. On sufficient conditions for stability independent of delay. IEEE Trans. Automat. Control. 40:1995;1675-1680.
27. Kim J. H. Robust stability of linear systems with delayed perturbations. IEEE Trans. Automat. Control. 41:1996;1820-1822.
28. Jeung E. T., Oh D. C., Kim J. H., Park H. B. Robust controller design for uncertain systems with time delays: LMI approach. Automatica. 33:1996;1229-1231.
29. Luo J. S., van den Bosch P. P. J. Independent of delay stability criteria for uncertain linear state space models. Automatica. 33:1997;171-179.
30. Hmamed A. Further results on the robust stability of linear systems including delayed perturbations. Automatica. 33:1997;1763-1765.
31. Gu K. Discretized LMI set in the stability problem of linear uncertain time-delay systems. Internat. J. Control. 68:1997;923-934.
32. K. H. Lee, Y. S. Moon, and W. H. Kwon, Robust stability analysis of parametric uncertain time-delay systems, inProc. 37th CDC, Tampa, FL, 1998, Vol. 2, pp. 1346-1351.
33. Kolmanovskii V. B., Niculescu S. I., Richard J. P. On the Liapunov-Krasovskii functional for stability analysis of linear delay systems. Internat. J. Control. 72:1999;374-384.
34. Kolmanovskii V. B., Richard J. P. Stability of some linear systems with delays. IEEE Trans. Automat. Control. 44:1999;984-989.
35. Xu B., Liu Y. An improved Razumikhin-type theorem and its applications. IEEE Trans. Automat. Control. 39:1994;839-841.
36. Xu B. Comments on "Robust stability of delay dependence for linear uncertain systems," Author's reply. IEEE Trans. Automat. Control. 39:1994;2365.
37. Xu B. Author's reply. IEEE Trans. Automat. Control. 42:1997;430.
38. Xu B., Fu Y., Bai L. Further results on robust bounds for large-scale time-delay systems with structured and unstructured uncertainties. Internat. J. Systems Sci. 27:1996;1491-1495.
39. Xu B. Stability robustness bounds for linear systems with multiple time-varying delayed perturbations. Internat. J. Systems Sci. 28:1997;1311-1317.
40. B. Xu, N & S conditions for exponential stability of retarded dynamic systems and some applications, inProc. 1998 ACC, Philadelphia, FL, 1998, Vol. 3, pp. 1953-1957.
41. B. Xu, Stability of time-delay systems. (1). Exponential stability of retarded dynamic systems, inProc. IEEE Hong Kong Symposium on Robotics and Control, Hong Kong, China, 1999, Vol. 2, pp. 719-724.
42. B. Xu, Stability of time-delay systems. (2). Numerically tractable α-stability criteria for linear time-invariant systems with multiple delays, Proc. IEEE Hong Kong Symposium on Robotics and Control, Hong Kong, China, 1999, Vol. 2, pp. 725-730.
43. Xu B. Decay estimates for retarded dynamic systems. Internat. J. Systems Sci. 30:1999;427-439.
44. Xu B. Necessary and sufficient conditions of generalized exponential stability for retarded dynamic systems. Control Theory Appl. 16:1999;802-806.
45. B. Xu, Stability criteria for linear time-invariant systems with multiple delays, J. Math. Anal. Appl, in press.
46. Xu B., Lam J. Decentralized stabilization of large-scale interconnected time-delay systems. J. Optim. Theory Appl. 103:1999;231-240.
47. Xu B. Decentralized stabilization of large-scale linear continuous systems with N × N time-varying delays. Internat. J. Systems Sci. 31:2000;489-496.
48. Webster R. Convexity. 1994;Oxford Univ. Press, Oxford/New York/Tokyo.
49. Boyd S., Ghaoui L. E., Feron E., Balakrishnan V. Linear Matrix Inequalities in Systems and Control Theory. 1994;SIAM, Philadelphia.
50. P. Gahinet, A. Nemirovski, A. J. Laub, and, M. Chilali, LMI Control Toolbox for Use with MATLAB, The Math Works, Inc, 1995.