Saturated Markovian Switching Systems

Introduction

Linear systems with Markovian jumping parameters, which are a class of switching systems with a switching sequence of Markovian nature, offer the advantage to model large varieties of physical phenomena. This class of systems has been used successfully to model manufacturing systems, power systems, economic systems, etc.We refer the reader, for example to [52] and references therein. It is well known that all these physical systems admit inputs limitation which are modeled by constraints of inequality type. The problem of stochastic stability of discrete-time linear systems with both Markovian jumping parameters and constrained control have been first investigated by [51] for systems without delay while systems with delay were studied in [74].