Stabilization of continuous-time singularly perturbed switched systems

In this article, stability of continuous-time switched linear systems in the singular perturbation form is investigated. We show that the stability of slow and fast switched subsystems is not a sufficient condition for stability of the corresponding two-time scale switched system, under an arbitrary switching law. Thus, LMI conditions to design a state-feedback control law stabilizing continuous-time singularly perturbed switched linear systems are proposed.

[1]  A. Morse.  Supervisory control of families of linear set-point controllers , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[2]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[3]  Brian Ingalls,et al.  Exponential stability of singularly perturbed switched systems with time delay , 2008 .

[4]  Robert Shorten,et al.  Stability Criteria for Switched and Hybrid Systems , 2007, SIAM Rev..

[5]  Clyde F. Martin,et al.  A Converse Lyapunov Theorem for a Class of Dynamical Systems which Undergo Switching , 1999, IEEE Transactions on Automatic Control.

[6]  P. Kokotovic,et al.  Singular perturbation method for reducing the model order in optimal control design , 1968 .

[7]  R. Decarlo,et al.  Perspectives and results on the stability and stabilizability of hybrid systems , 2000, Proceedings of the IEEE.

[8]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[9]  Desineni S Naidu,et al.  Singular perturbations and time scales in control theory and applications: An overview , 2002 .

[10]  Germain Garcia,et al.  The Infinite Time Near Optimal Decentralized Regulator Problem for Singularly Perturbed Systems: A Convex Optimization Approach , 1998 .

[11]  Hassan K. Khalil,et al.  Singular perturbation methods in control : analysis and design , 1986 .

[12]  Ivan Malloci.  Two time scale switched systems: An application to steering control in hot strip mills , 2009 .

[13]  A. Michel,et al.  Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[14]  P. Kokotovic.  A Riccati equation for block-diagonalization of ill-conditioned systems , 1975 .

[15]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).