Piecewise lyapunov functions for switched systems with average dwell time

Asian Journal of Control

Volumn 2, Issue 3, 2000, Pages 192-197

  Zhai, Guisheng ^a   Hu, Bo ^b   Yasuda, Kazunori ^a   Michel, Anthony N ^b  

^a WAKAYAMA UNIVERSITY   (Japan)

^b UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

Average dwell time; Exponential stability; Perturbations; Piecewise lyapunov function; Switched system; Switching law

Indexed keywords

EID: 0013221142     PISSN: 15618625     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1934-6093.2000.tb00157.x     Document Type: Article

References (16)

1. Morse, A.S., "Supervisory Control of Families of Linear Set-Point Controllers-Part 1: Exact Matching," IEEE Trans. Automat. Contr., Vol. 41, No. 10, pp. 1413-1431 (1996).
2. Liberzon, D. and A.S. Morse, "Basic Problems in Stability and Design of Switched Systems," IEEE Contr. Syst. Mag., Vol. 19, No. 5, pp. 59-70 (1999).
3. Dayawansa, W.P. and C.F. Martin, "A Converse Lyapunov Theorem for a Class of Dynamical Systems Which Undergo Switching," IEEE Trans. Automat. Contr., Vol. 44, No. 4, pp. 751-760 (1999).
4. Hu, B., G. Zhai and A.N. Michel, "Hybrid Output Feedback Stabilization of Two-Dimensional Linear Control Systems," Proc. Amer. Contr. Conf., Chicago, U.S.A., pp. 2184-2188 (2000).
5. Hu, B. and A.N. Michel, "Stability Analysis of Digital Feedback Control Systems with Time-Varying Sampling Periods," Automation, Vol. 36, pp. 897-905 (2000).
6. Hespanha, J.P. and A.S. Morse, "Stability of Switched Systems with Average Dwell-Time," Proc. The 38th IEEE Conf. Decis. Contr., Phoenix, U.S.A., pp. 2655-2660(1999).
7. Hu, B., X. Xu, A.N. Michel and P.J. Antsaklis, "Stability Analysis for a Class of Nonlinear Switched Systems," Proc. The 38th IEEE Conf. Decis. Contr., Phoenix, U.S.A., pp. 4374-4379 (1999).
8. Narendra, K.S. and J. Balakrishnan, "A Common Lyapunov Function for Stable LTI Systems with Commuting A-Matrices," IEEE Trans. Automat. Contr., Vol. 39, No. 12, pp. 2469-2471 (1994).
9. Feron, E., "Quadratic Stabilizability of Switched Systems via State and Output Feedback," to appear in SIAM J. Contr. Optimiz.
10. Branicky, M.S., "Multiple Lyapunov Functions and Other Analysis Tools for Switched and Hydrid Systems," IEEE Trans. Automat. Contr., Vol. 43, No. 4, pp. 475-482 (1998).
11. Ye, H., A.N. Michel and L.'Hou, "Stability Theory for Hybrid Dynamical Systems," IEEE Trans. Automat. Contr., Vol. 43, No. 4, pp. 461-474 (1998).
12. Pettersson, S. and B. Lennartson, "LMI for Stability and Robustness of Hybrid Systems," Proc. Amer. Contr. Conf., New Mexico, U.S.A., pp. 1714-1718 (1997).
13. Wicks, M.A., P. Peleties and R.A. DeCarlo, "Construction of Piecewise Lyapunov Functions for Stabilizing Switched Systems," Proc. The 33rd IEEE Conf. Decis. Contr., Florida, U.S.A., pp. 3492-3497 (1994).
14. Zhai, G., B. Hu, K. Yasuda and A.N. Michel, "Stability Analysis of Switched Systems with Stable and Unstable Subsystems: An Average Dwell Time Approach," Proc. Amer. Contr. Conf., Chicago, U.S.A., pp. 200-204 (2000).
15. Boyd, S., L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, U.S.A. (1994).
16. Gahinet, G., A. Nemirovski, A.J. Laub and M. Chilali, LMI Control Toolbox for Use with Matlab, the MathWorks Inc., Massachusetts, U.S.A. (1995).