Robust Stabilization for a Class of Switched Nonlinear Systems

Abstract:

This paper addresses the stabilization problem for a class of switched nonlinear systems with Lipschitz nonlinearities using the multiple Lyapunov functions (MLFs) approach. A state feedback controller and a state dependent switching law are proposed to asymptotic stabilization the switched system via linear matrix inequalities (LMI). The developed control strategy ensures asymptotic stability of the closed-loop system even if the nonlinear part . Finally, the feasibility of the proposed method is illustrated through a simulation example

• Periodical: Advanced Materials Research (Volumes 490-495)
• Pages: 1536-1540
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.490-495.1536
• Online since: March 2012
• Authors: Cai Yun Wu, Ben Niu
• Keywords: Linear Matrix Inequality (LMI), Multiple Lyapunov Functions, Stabilization, Switched Nonlinear Systems

References

[1] D. Liberzon, A.S. Morse: Basic problems in stability and design of switched systems, IEEE Trans. Automat. Control 19 (5) (1999) ,P. 59–70.

[2] D. Liberzon: Switching in Systems and Contro. (Birkhauser, Boston, 2003).

[3] J. Daafouz, P. Riedinger, C. Iung: Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach, IEEE Trans. Automat. Control 47 (11) (2002) ,P. 1883–1887.

DOI: 10.1109/tac.2002.804474

[4] D. Liberzon, R. Tempo: Common Lyapunov functions and gradient algorithms, IEEE Transactions on Automatic Control 49 (6), (2004) , P. 990-994.

DOI: 10.1109/tac.2004.829632

[5] R. Shorten, K.S. Narendra, O. Mason: A result on common quadratic Lyapunov functions, IEEE Transactions on Automatic Control 48 (1), (2003) ,P. 110-113.

DOI: 10.1109/tac.2002.806661

[6] J.P. Hespanha, A.S. Morse: Stability of switched systems with average dwell-time, in Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, AZ, 1999,P. 655-2660.

DOI: 10.1109/cdc.1999.831330

[7] Z.D. Sun, S.S. Ge: Analysis and synthesis of switched linear control systems, Automatica 41 (2) , (2005), P. 181–195.

DOI: 10.1016/j.automatica.2004.09.015

[8] M.S. Branicky: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Trans. Automat. Control 43 (4) , (1998), P. 475–482.

DOI: 10.1109/9.664150

[9] G. S. Deaecto, J. C. Geromel, and J. Daafouz: Dynamic output feedback H1 control of switched linear systems, Automatica, 47(8), ( 2011),P. 1713–1720.

DOI: 10.1016/j.automatica.2011.02.046

[10] J. Zhao, and D. J. Hill: On stability, L2-gain and control for switched systems, Automatica, 44(5), (2008),P. 1220–1232.

[11] H. Yang, V. Cocquempot, and B. Jiang: On stabilization of switched nonlinear systems with unstable modes, Systems and Control Letter, 58(10-11), ( 2009),P. 703–708.

DOI: 10.1016/j.sysconle.2009.06.007

[12] Z. R. Xiang, Y. N. Sun, and Q. W. Chen: Robust reliable stabilization of uncertain switched neutral systems with delayed switching, Applied Mathematics and Computation, 217(23), (2011),P. 9835–9844.

DOI: 10.1016/j.amc.2011.04.082

[13] L. I. Allerhand, and U. Shaked: Robust stability and stabilization of linear switched systems with dwell time, IEEE Trans. on Automatic Control, 56(2),P. (2011), P. 381–386.

DOI: 10.1109/tac.2010.2097351

[14] Q. K. Li, J. Zhao, and G. M. Dimirovski: Robust tracking control for switched linear systems with time-varying delays, IET Control Theory and Applications, 2(6), (2008), P. 449–457.

DOI: 10.1049/iet-cta:20070344