Stabilization of Discrete-Time Switched Linear Systems: A Control-Lyapunov Function Approach

Authors:
Wei Zhang;Alessandro Abate;Jianghai Hu
Affiliations:
School of Electrical and Computer Engineering, Purdue University, USA IN 47907;Department of Aeronautics and Astronautics, Stanford University, USA CA 94305;School of Electrical and Computer Engineering, Purdue University, USA IN 47907
Venue:
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Year:
2009

Citing 4
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Abstract

This paper studies the exponential stabilization problem for discrete-time switched linear systems based on a control-Lyapunov function approach. A number of versions of converse control-Lyapunov function theorems are proved and their connections to the switched LQR problem are derived. It is shown that the system is exponentially stabilizable if and only if there exists a finite integer N such that the N -horizon value function of the switched LQR problem is a control-Lyapunov function. An efficient algorithm is also proposed which is guaranteed to yield a control-Lyapunov function and a stabilizing strategy whenever the system is exponentially stabilizable.