Summary: Stabilization of Discrete-Time Switched Linear Systems:
A Control-Lyapunov Function Approach
, Alessandro Abate2
and Jianghai Hu1
School of Electrical and Computer Engineering, Purdue University, IN 47907, USA.
Department of Aeronautics and Astronautics, Stanford University, CA 94305, USA.
Abstract. This paper studies the exponential stabilization problem for
discrete-time switched linear systems based on a control-Lyapunov func-
tion approach. A number of versions of converse control-Lyapunov func-
tion theorems are proved and their connections to the switched LQR
problem are derived. It is shown that the system is exponentially stabiliz-
able 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 func-
tion. An efficient algorithm is also proposed which is guaranteed to yield
a control-Lyapunov function and a stabilizing strategy whenever the sys-