Stability of switched systems with time delay

Nonlinear Analysis: Hybrid Systems

Volumn 1, Issue 1, 2007, Pages 44-58

  Zhang, Yi ^a   Liu, Xinzhi ^b   Shen, Xuemin ^b  

^a CHINA UNIVERSITY OF PETROLEUM   (China)

^b UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 36549062962     PISSN: 1751570X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nahs.2006.03.001     Document Type: Article

References (27)

1. A.A. Agrachev, Lie-algebraic conditions for exponential stability of switched systems, in: Proc. IEEE CDC, 1999, pp. 2679-2684
2. O. Beldiman, L. Bushnell, Stability, linearization and control of switched systems, in: Proc. IEEE ACC, 1999, pp. 2950-2954
3. M.S. Branicky, Stability of switched and hybrid systems, in: Proc. IEEE CDC, 1994, pp. 3498-3503
4. M.S. Branicky, Studies in hybrid systems: Modeling, analysis, control, ScD Thesis, MIT EECS, 1995
5. Dayawansa W.P., and Martin C.F. A converse Lyapunov theorem for a class of dynamical systems which undergo switching. IEEE Trans. Automat. Control 44 (1999) 751-760
6. G. Davrazos, N.T. Koussoulas, A review of stability results for switched and hybrid systems, in: Proc. of 9th Mediterranean Conference on Control and Automation, MED, 2001
7. M. Dogruel, U. Ozguner, Stability of a set of matrices: An application to hybrid systems, in: Proc. IEEE Int. Symposium on Intelligent Control, 1995
8. Fierro R., and Lewis F.L. A framework for hybrid control design. IEEE Trans. Syst. Man Cyb. A 27 (1997) 765-773
9. R. Fierro, F.L. Lewis, C.T. Abdallah, Common, multiple, and parametric Lyapunov functions for a class of hybrid dynamical systems, in: Proc. IEEE Mediterranean Symposium on New Directions in Control and Automation, June 1996, pp. 77-82
10. R. Fierro, A hybrid system approach to a class of intelligent control systems, Ph.D. Thesis, Univ. of Texas at Arlington, August 1997
11. B. Hu, X. Xu, A.N. Michel, J.P. Antsaklis, Stability analysis for a class of nonlinear switched systems, in: Proc. IEEE CDC, 1999, pp. 4374-4379
12. Hocherman-Frommer J., Kulkarni S.R., and Ramadge P.J. Controller switching based on output prediction errors. IEEE Trans. Automat. Control 43 (1998) 596-607
13. Hespanha J. Uniform stability of switched linear systems: Extensions of LaSalle's invariance principle. IEEE Trans. Automat. Control 49 (2004) 470-482
14. J. Hespanha, A.S. Morse, Stability of switched systems with average dwell-time, in: Proc. IEEE CDC, 1999, pp. 2655-2660
15. Liberzon D., Hespanha J.P., and Morse A.S. Stability of switched systems: A Lie-algebraic condition. Systems Control Lett. 37 3 (1999) 117-122
16. Liberzon D., and Morse A.S. Basic problems in stability and design of switched systems. IEEE Control Syst. Mag. 19 5 (1999) 59-70
17. Branicky M.S. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automat. Control 43 4 (1998) 475-482
18. Narendra K.S., and Balakrishnan J. A common Lyapunov function for stable LTI systems with commuting A-matrices. IEEE Trans. Automat. Control 39 (1994) 2469-2471
19. Pait F.M., and Kassab J. Parallel algorithms for adaptive control: Robust stability. In: Morse A.S. (Ed). Control Using Logic-Based Switching (1997), Springer-Verlag, London
20. S. Pettersson, B. Lennartson, Stability and robustness for hybrid systems, in: Proc. IEEE CDC, 1996, pp. 1202-1207
21. S. Pettersson, B. Lennartson, Exponential stability of hybrid systems using piecewise quadratic Lyapunov functions resulting in LMIs, in: Proc. 14th Triennial World Congress, 1999
22. S. Pettersson, Analysis and design of hybrid systems, Ph.D. Thesis, Chalmers Univ. of Technology, 1999
23. R.N. Shorten, K.S. Naredra, On the stability and existence of common Lyapunov functions for stable linear switching systems, in: Proc. IEEE CDC, 1998, pp. 3723-3724
24. Solo V. On the stability of slowly time-varying linear systems. Math. Control Signals Systems 7 (1994) 331-350
25. C.J. Tomlin, S.S. Sastry, Switching through singularities, in: Proc. IEEE CDC, 1997, pp. 1-6
26. Wick M.A., Peleties P., and Decarlo R.A. Switched controller synthesis for the quadratic stabilization of a pair of unstable linear systems. Eur. J. Control 4 (1998) 140-147
27. Zhai G., Hu B., Yasuda K., and Michel A.N. Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach. J. Systems Sci. 8 32 (2001) 1055-1061