Exponential stabilization of discrete-time switched linear systems

Journal article

This article studies the exponential stabilization problem for discrete-time switched linear systems based on a control-Lyapunov function approach. It is proved that a switched linear system is exponentially stabilizable if and only if there exists a piecewise quadratic control-Lyapunov function. Such a converse control-Lyapunov function theorem justifies many of the earlier synthesis methods that have adopted piecewise quadratic Lyapunov functions for convenience or heuristic reasons. In addition, it is also proved that if a switched linear system is exponentially stabilizable, then it must be stabilizable by a stationary suboptimal policy of a related switched linear-quadratic regulator (LQR) problem. Motivated by some recent results of the switched LQR problem, an efficient algorithm is proposed, which is guaranteed to yield a control-Lyapunov function and a stabilizing policy whenever the system is exponentially stabilizable. © 2009 Elsevier Ltd. All rights reserved.

Authors: Zhang, W; Abate, A; Hu, J; Vitus, M

• Journal: Automatica
• Volume: 45
• Issue: 11
• Pages: 2526-2536
• Publication date: 2009-11-01
• DOI: 10.1016/j.automatica.2009.07.018
• ISSN: 0005-1098
• Language: English
• Keywords: Switching stabilization; Control-Lyapunov functions; Switched systems; Piecewise quadratic Lyapunov functions; Optimal control