A Mean Square Stability Test for Markovian Jump Linear Systems

Abstract

This paper proposes a test for the mean square stability problem for discrete-time linear systems subject to random jumps in the parameters, described by an underlying finite-state Markov chain. In the model studied, the horizon of the problem is given by a stopping time , associated with the occurrence of a crucial failure after which the system is brought to a halt for maintenance. The usual stochastic stability concepts and associated results are not indicated, since they are tailored to purely infinite horizon problems. Using the concept named stochastic -stability, equivalent conditions to ensure the stochastic stability of the system until the occurrence of is obtained. These conditions lead to a test that benefits from the chain structure for proposing a simpler decomposition algorithm for the mean square stability verification for infinite horizon problems.