Stabilization of switched linear systems with time-varying delay in switching occurrence detection

Circuits, Systems, and Signal Processing

Volumn 26, Issue 3, 2007, Pages 361-377

  Ji, Zhijian ^a   Guo, Xiaoxia ^b   Xu, Shixu ^a   Wang, Long ^c  

^a QINGDAO UNIVERSITY   (China)

^b OCEAN UNIVERSITY OF CHINA   (China)

^c PEKING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

FEEDBACK CONTROL; LINEAR SYSTEMS; STABILIZATION; TIME DELAY;

SWITCHED LINEAR SYSTEMS; SWITCHING OCCURENCE DETECTION;

SWITCHING SYSTEMS;

EID: 34547440165     PISSN: 0278081X     EISSN: 15315878     Source Type: Journal    
DOI: 10.1007/s00034-006-0414-x     Document Type: Article

References (26)

1. A. Bacciotti, Stabilization by means of state space depending switching rules, Syst. Contr. Lett., 53, 195-201, 2004.
2. M. S. Branicky, Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Trans. Automat. Control, 43, no. 4, 475-482, 1998.
3. D. Cheng, L. Guo, Y. Lin, and Y. Wang, A note on overshoot estimation in pole-placement, J. Control Theory Appl., 2, no. 2, 161-164, 2004.
4. D. Cheng, L. Guo, Y. Lin, and Y. Wang, Stabilization of switched linear systems, IEEE Trans. Automat. Control, 50, no. 5, 661-666, 2005.
5. R. A. DeCarlo, M. S. Branicky, S. Pettersson, and B. Lennartson, Perspectives and results on the stability and stabilizability of hybrid systems, Proc. IEEE, 88, no. 7, 1069-1082, 2000.
6. J. P. Hespanha, Uniform stability of switched linear systems: Extensions of LaSalle's invariance principle, IEEE Trans. Automat. Control, 49, no. 4, 470-482, 2004.
7. J. P. Hespanha and A. S. Morse, Stability of switched systems with average dwell-time, Proc. 38th IEEE Conference on Decision and Control, Phoenix, AZ, 2655-2660, 1999.
8. H. Ishii, T. Basar, and R. Tempo, Randomized algorithms for synthesis of switching rules for multimodal systems, IEEE Trans. Automat. Control 50, no. 6, 754-767, 2005.
9. Z. Ji, L. Wang, G. Xie, and F. Hao, Linear matrix inequality approach to quadratic stabilisation of switched systems, IEE Proc.-Control Theory Appl., 151, no. 3, 289-294, 2004.
10. Z. Ji, L. Wang, and G. Xie, Quadratic stabilization of switched systems, Int. J. System Science, 36, no. 7, 395-404, 2005.
11. C. King and R. Shorten, On the design of stable state dependent switching laws for single-input single-output systems, Proc. 44th IEEE Conference on Decision and Control, and the European Control Conference, Seville, Spain, 4863-4866, December 12-15, 2005.
12. X. D. Koutsoukos and P. J. Antsaklis, Design of stabilizing switching control laws for discrete and continuous-time linear systems using piecewise-linear Lyapunov functions, Int. Journal of Control, 75, no. 12, 932-945, 2002.
13. D. Liberzon and A. S. Morse, Basic problems in stability and design of switched systems, IEEE Control Syst. Mag., 19, no. 5, 59-70, 1999.
14. H. Lin and P. J. Antsaklis, A converse Lyapunov theorem for uncertain switched linear systems, Proc. 44th IEEE Conference on Decision and Control, and the European Control Conference, Seville, Spain, 3291-3296, December 12-15, 2005.
15. A. S. Morse, Supervisory control of families of linear set-point controllers, part 2: Robustness. IEEE Trans. Automat. Control, 42, 1500-1515, 1997.
16. E. D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, 2nd ed., Springer-Verlag, New York, 1998.
17. Z. Sun, A general robustness theorem for switched linear systems, Proc. 2005 IEEE International Symposium on Intelligent Control, Limassol, Cyprus, 8-11, June 27-29, 2005.
18. Z. Sun and S. S. Ge, Analysis and synthesis of switched linear control systems, Automatica, 41, no. 2, 181-195, 2005.
19. M. Wicks, P. Peleties, and R. A. DeCarlo, Switched controller synthesis for the quadratic stabilization of a pair of unstable linear systems, European Journal of Control, 4, no. 2, 140-147, 1998.
20. G. Xie and L. Wang, Stabilization of switched linear systems with time-delay in detection of switching signal, J. Math. Anal. Appl., 305, 277-290, 2005.
21. H. Ye, A. N. Michel, and L. Hou, Stability theory for hybrid dynamical systems, IEEE Trans. Automat. Control, 43, no. 4, 461-474, 1998.
22. C. A. Yfoulis and R. Shorten, A numerical technique for the stability analysis of linear switched systems, Int. J. Contr., 77, no. 11, 1019-1039, 2004.
23. G. Zhai, B. Hu, K. Yasuda, and A. N. Michel, Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach, Int. J. System Science, 32, no. 8, 1055-1061, 2001.
24. G. Zhai, H. Lin, and P. J. Antsaklis, Quadratic stabilizability of switched linear systems with polytopic uncertainties, Int. J. Contr. 76, pp. 747-753, 2003.
25. J. Zhao and G. M. Dimirovski, Quadratic stability of a class of switched non-linear systems, IEEE Trans. Automat. Control, 49, 574-578, 2004.
26. 2-gain for switched systems, Proc. 44th IEEE Conference on Decision and Control, and the European Control Conference, Seville, Spain, 3279-3284, December 12-15, 2005.