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Summary: Stabilization of Discrete-Time Switched Linear Systems:
A Control-Lyapunov Function Approach
Wei Zhang1
, Alessandro Abate2
and Jianghai Hu1
1
School of Electrical and Computer Engineering, Purdue University, IN 47907, USA.
{zhang70,jianghai@purdue.edu}
2
Department of Aeronautics and Astronautics, Stanford University, CA 94305, USA.
{aabate@stanford.edu}
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-
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