Abstract
This paper is concerned with the robust stability and stabilization for a class of switched discrete-time systems with state parameter uncertainty. Firstly, a new matrix inequality considering uncertainties is introduced and proved. By means of it, a novel sufficient condition for robust stability and stabilization of a class of uncertain switched discrete-time systems is presented. Furthermore, based on the result obtained, the switching law is designed and has been performed well, and some sufficient conditions of robust stability and stabilization have been derived for the uncertain switched discrete-time systems using the Lyapunov stability theorem, block matrix method, and inequality technology. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.
Highlights
1 Introduction A switched system is a hybrid dynamical system consisting of a finite number of subsystems and a logical rule that manages switching between these subsystems
Switched systems have drawn a great deal of attention in recent years; see [ – ] and references therein
Two different linear matrix inequality-based conditions allow to check the existence of such a Lyapunov function
Summary
A switched system is a hybrid dynamical system consisting of a finite number of subsystems and a logical rule that manages switching between these subsystems. The problem of stability analysis and control synthesis of switched systems in the discrete-time domain was addressed in [ ]. Two different linear matrix inequality-based conditions allow to check the existence of such a Lyapunov function. Sufficient delay-dependent existence conditions of the H∞ fault estimator were given in terms of certain matrix inequalities based on the average dwell-time approach.
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