Some remarks on the stability of linear systems with delayed state

Proceedings of the IEEE Conference on Decision and Control

Volumn 1, Issue , 1998, Pages 299-304

  Kolmanovskii, Vladimir B ^a   Niculescu, Silviu Iulian ^a   Richard, Jean Pierre ^a  

^a RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

DELAYED STATES; LYANUPOV-KRASOVSKII FUNCTIONAL;

ASYMPTOTIC STABILITY; CONTROL SYSTEM ANALYSIS; DIFFERENTIAL EQUATIONS; LYAPUNOV METHODS; SYSTEM STABILITY;

LINEAR CONTROL SYSTEMS;

EID: 0032259990     PISSN: 01912216     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Article

References (31)

1. F. G. Boese, "Stability in a special class of retarded difference-differential equations with interval-valued parameters," J. Math. Anal. Appl., 181, pp. 367-386, 1989.
2. F. G. Boese, "Stability criteria for second-order dynamical systems involving several time-delays," SIAM J. Math. Anal, 26, pp. 1306-1330. 1995.
3. S. Boyd, L. El Ghaoui, E. Feron and V. Balakr-ishnan. Linear matrix inequalities in system and control theory. SIAM, Philadelphia. 1994.
4. S. A.Campbell and J. Bélair, "Multiple-delayed differential equations as models for biological control systems."' Proc. World Math. Conf. pp. 3110-3117. 1993.
5. J. Chen and H. A. Latchman, "Asymptotic stability independent of delays: simple necessary and sufficient conditions," Proc. 1994 Amer. Contr. Conf., Baltimore, U.S.A., pp. 1027-1031, 1994.
6. O. Diekmann, S. A. van Gils, S. M. Verduyn-Lunel and H. Walther, Delay equations, Functional, Complex and Nonlinear Analysis, Springer-Verlag, New York, 1995.
7. M. Fu, H. Li and S. -I. Niculescu, "Robust stability and stabilization of time-delay system via integral quadratic constraint approach," in Stability and Control of Time-Delay Systems (L. Dugard and E. I. Verriest, Eds.), LNCIS, Springer-Verlag, London, 228, pp. 101-116, 1997.
8. A. Goubet-Bartholoméüs, M. Dambrine and J. -P. Richard, "Stability of perturbed systems with time-varying delays," Syst. & Contr. Lett., 31, pp. 155-163, 1997.
9. J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations. Springer-Verlag, New York, 1993.
10. J. K. Hale, E. F. Infante and F. S. P. Tsen, "Stability in linear delay equations," J. Math. Anal. Appi, 105, pp. 533-555, 1985.
11. J. K. Hale and W. Huang, "Global geometry of the stable regions for two delay differential equations," J. Math. Anal. Appl., 178, pp. 344-362, 1993.
12. D. Hertz, E. I. Jury and E. Zeheb, "Stability independent and dependent of delay for delay differential systems," J. Franklin Inst., 318, pp. 143-150, 1984.
13. E. W. Kamen, "Linear systems with commensurate time delays: Stability and stabilization independent of delay," IEEE Trans. Automat. Contr., AC-27, pp. 367-375, 1982; corrections in IEEE Trans. Automat. Contr., AC-28, pp. 248-249, 1983.
14. V. B. Kolmanovskii, "The stability of certain systems with arbitrary aftereffects," Dokl. Russ. Akad. Nauk, 331, 4, pp. 421-424, 1993.
15. V. B. Kolmanovskii and A. D. Myshkis, Applied Theory of functional differential equations, Kluwer, 1992.
16. V. B. Kolmanovskii, S. -I. Niculescu and J. -P. Richard, "," Internal Note HeuDiaSyC'97, 1997 (the full version of the paper).
17. V. B. Kolmanovskii, S. -I. Niculescu and .J. -P. Richard. "On the Liapunov-Krasovskii functional for stability analysis of linear delay systems," Int. J. Contr. (accepted for publication. May 1998).
18. V. B, Kolmanovskii, J. P. Richard and A. Ph. Tchangani. "Stability of linear systems with discrete-plus-distributed delays; .Application to some model transformations." MTNS'08. Padoue, Italy, 1998.
19. X. Li and C. E. de Souza, "LMI approach to delay-dependent robust stability and stabilization of uncertain linear delay systems," in Proc. 34th IEEE CDC, New Orleans, Louisiana, U.S.A., pp. 3614-3619, 1995.
20. M. Malek-Zavarei and M. Jamshidi, Time Delay Systems: Analysis, Optimization and Applications, North-Holland Syst. Contr. Series, Amsterdam, 1987.
21. T. Mori, "Criteria for asymptotic stability of linear time-delay systems," IEEE Trans. Automat. Contr., AC-30, pp. 158-160, 1985.
22. S. I. Niculescu, Systèmes à retard. Aspects qualitatifs sur la stabilité et la stabilisation, Diderot, Paris, 'Nouveaux Essais' Series, 1997.
23. S. I. Niculescu, C. E. de Souza, J. -M. Dion and L. Dugard, "Robust stability and stabilization for uncertain linear systems with state delay: Single delay case (I), Multiple delays case (II)," in Proc. IFAC Workshop on Robust Control Design, Rio de Janeiro, Brazil, pp. 469-474, pp. 475-480, 1994.
24. S. I. Niculescu, C. E. de Souza, L. Dugard and J. -M. Dion, "Robust exponential stability of uncertain linear systems with time-varying delays," in Proc. 3rd European Contr. Conf, Rome, Italy, pp. 1802-1807, 1995.
25. S. I. Niculescu, J. -M. Dion and L. Dugard, "Delays-dependent stability for linear systems with several delays: An LMI approach," in Proc. 13th IFAC World 1996, San Francisco, US, 1996.
26. S. I. Niculescu, A. Trofino-Neto, J. -M. Dion and L. Dugard, "Delay-dependent stability of linear systems with delayed state: An L.M.I, approach," in Proc. 34th IEEE CDC, New Orleans, Louisiana, US, pp. 1495-1497, 1995.
27. S. I. Niculescu, E. I. Verriest, L. Dugard and J. M. Dion, Stability and robust stability of time-delay systems: A guided tour, in Stability and Control of Time-Delay Systems (L. Dugard and E. I. Verriest, Eds.), LNCIS, Springer-Verlag, London, 228, pp. 1-71, 1997.
28. J. P. Richard, A. Goubet-Bartholoméüs, P. A. Tchangani and M. Dambrine, "Nonlinear delay systems: Tools for quantitative approach to stabilization," in in Stability and Control of Time-Delay Systems (L. Dugard and E. I. Verriest, Eds.), LNCIS, Springer-Verlag, London, 228, pp. 218-240. 1997.
29. G. M. Schoen and H. P. Geering, "Stability condition for a delay differential system." Int. J. Contr., 58, pp. 247-252, 1993.
30. G. Stépan. Retarded dynamical systems: stability and characteristic function. John Wiley & Sons. 1989.
31. J. H. Su. "Further results on the robust stability of linear systems with a single delay." Syst. & Contr. Lett. 23. pp. 375-379, 1994.