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Summary: Stabilization and Performance Analysis for a Class of Switched Systems
Lei Fang, Hai Lin, and Panos J. Antsaklis
Abstract-- This paper investigates stability and control de-
sign problems with performance analysis for discrete-time
switched linear systems. The switched Lyapunov function
method is combined with Finsler's Lemma to generate var-
ious tests in the enlarged space containing both the state
and its time difference, allowing extra degree of freedom
for stability analysis and control design. Two performance
measures being considered are the decay rate and the input-
output performance. A new LMI based stability test for the
existence of switched Lyapunov functions is first developed.
If a switched Lyapunov function exists, asymptotic stability
of the switched system also implies its exponential stability.
An LMI optimization problem is then formulated to find a
bound on the decay rate of the system. To attain the bound,
state feedback control gains are designed. Using the same
framework and the well-known S-procedure, a generalized
sufficient LMI condition is obtained which guarantees a -
performance of the closed-loop switched systems subject to
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