Stability analysis of switched time delay systems

SIAM Journal on Control and Optimization

Volumn 47, Issue 2, 2008, Pages 936-949

  Yan, Peng ^a   Özbay, Hitay ^b  

^a SEAGATE TECHNOLOGY   (United States)

^b BILKENT UNIVERSITY   (Turkey)

Author keywords

Asymptotic stability; Dwell time; Switched systems; Time delay

Indexed keywords

DWELL TIME; DWELL TIMES; INFINITE NUMBERS; LYAPUNOV; NUMERICAL EXAMPLES; PAPER ADDRESSES; PIECE WISES; RAZUMIKHIN FUNCTIONS; STABILITY ANALYSES; SUFFICIENT CONDITIONS; SWITCHED SYSTEMS; TIME INVARIANTS; TIME- DELAYS; TIME-DELAY SYSTEMS;

ASYMPTOTIC ANALYSIS; ASYMPTOTIC STABILITY; SWITCHING FUNCTIONS; TIME DELAY;

SYSTEM STABILITY;

EID: 55549132287     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/060668262     Document Type: Article

References (28)

1. C. BETT and M. LEMMON, Bounded amplitude performance of switched LPV systems with applications to hybrid systems, Automatica, 35 (1999), pp. 491-503.
2. C. DE PERSIS, R. DE SANTIS, and S. MORSE, Supervisory control with state-dependent dwell-time logic and constraints, Automatica, 40 (2004), pp. 269-275.
3. L. DUGARD and E. I. VERRIEST, eds., Stability and Control of Time-Delay Systems, Springer-Verlag, London, New York, 1998.
4. C. FOIAS, H. Özbay, and A. TANNENBAUM, Robust Control of Infinite Dimensional Systems: Frequency Domain Methods, Lecture Notes in Control and Inform. Sci. 209, Springer-Verlag, London, 1996.
5. K. GU and S.-I. NICULESCU, Survey on recent results in the stability and control of time-delay systems, ASME J. Dynamic Systems, Measurement, and Control, 125 (2003), pp. 158-165.
6. K. GU, V. L. KHARITNOV, and J. CHEN, Stability and Robust Stability of Time-Delay Systems, Birkhäuser, Boston, 2003.
7. J. HALE and S. VERDUYN LUNEL, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.
8. J. HESPANHA, Uniform stability of switched linear systems: Extension of LaSalle's invariance principle, IEEE Trans. Automat. Control, 49 (2004), pp. 470-482.
9. J. HESPANHA, D. LIBERZON, and S. MORSE, Overcoming the limitations of adaptive control by means of logic-based switching, Systems Control Lett., 49 (2003), pp. 49-65.
10. J. HESPANHA and S. MORSE, Stability of switched systems with average dwell-time, in Proceedings of the 38th Annual Conference on Decision and Control, Phoenix, AZ, 1999, pp. 2655-2660.
11. J. HOCHCERMAN-FROMMER, S. KULKARNI, and P. RAMADGE, Controller switching based on output prediction errors, IEEE Trans. Automat. Control, 43 (1998), pp. 596-607.
12. C. KAO and B. LINCOLN, Simple stability criteria for systems with time-varying delays, Automatica, 40 (2004), pp. 1429-1434.
13. F. KELLY, Mathematical modelling of the Internet, in Mathematics Unlimited-2001 and Beyond, B. Engquist and W. Schmid, eds., Springer-Verlag, Berlin, 2001, pp. 685-702.
14. V. L. KHARITONOV, Robust stability analysis of time delay systems: A survey, Ann. Rev. Control, 23 (1999), pp. 185-196.
15. V. L. KHARITONOV and D. HINRICHSEN, Exponential estimates for time delay systems, Systems Control Lett., 53 (2004), pp. 395-405.
16. V. KULKARNI, M. JUN, and J. HESPANHA, Piecewise quadratic Lyapunov functions for piecewise affne time delay systems, in Proceedings of the American Control Conference, Boston, MA, 2004, pp. 3885-3889.
17. D. LIBERZON and S. MORSE, Basic problems in stability and design of switched systems, IEEE Control Systems Mag., 19 (1999), pp. 59-70.
18. V. MONTAGNER, V. LEITE, S. TARBOURIECH, and P. PERES, Stability and stabilizability of discrete-time switched linear systems with state delay, in Proceedings of the American Control Conference, Portland, OR, 2005, pp. 3806-3811.
19. S. MORSE, Supervisory control of families of linear set-point controllers, part 1: Exact matching, IEEE Trans. Automat. Control, 41 (1996), pp. 1413-1431.
20. S.-I. NICULESCU, Delay Effects on Stability: A Robust Control Approach, Lecture Notes in Control and Inform. Sci. 269, Springer-Verlag, Heidelberg, 2001.
21. E. SKAFIDAS, R. EVANS, A. SAVKIN, and I. PETERSON, Stability results for switched controller systems, Automatica, 35 (1999), pp. 553-564.
22. Y. SUN, A MICHEL, and G. ZHAI, Stability of discontinuous retarded functional differential equations with applications to delay systems, in Proceedings of the American Control Conference, Denver, CO, 2003, pp. 3387-3392.
23. Y. SUN, A MICHEL, and G. ZHAI, Stability of discontinuous retarded functional differential equations with applications, IEEE Trans. Automat. Control, 50 (2005), pp. 1090-1105.
24. F. WU and K. GRIGORIADIS, LPV systems with parameter-varying time delays: Analysis and control, Automatica, 37 (2001), pp. 221-229.
25. ∞ controllers for a class of linear parameter varying systems, Systems Control Lett., 56 (2007), pp. 504-511.
26. ∞ performance analysis, in Advances in Communication Control Networks, S. Tarbouriech, C. Abdallah, and J. Chiasson, eds., Lecture Notes in Control and Inform. Sci. 308, Springer-Verlag, New York, 2005, pp. 49-64.
27. D. YUE and Q. HAN, Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching, IEEE Trans. Automat. Control, 50 (2005), pp. 217-222.
28. 2 gain analysis for switched symmetric systems with time delay, in Proceedings of the American Control Conference, Denver, CO, 2003, pp. 2682-2687.