Stability Analysis of Discrete-Time Stochastic Systems with Borel-Measurable Markov Jumps

摘要

This paper is devoted to stability analysis of discrete-time linear systems with Borel-measurable Markov jump parameters and independent multiplicative noises. The relationships are investigated among several stability concepts about the considered dynamics. Specifically, it is shown that strong exponential stability in the mean square sense can guarantee exponential stability, l_2 input-output stability and stochastic stability to hold. Moreover, both exponential stability and l_2 input-output stability give rise to stochastic stability. By a numerical example, it is demonstrated that Borel-measurable Markov jump systems must not be exponentially stable even if it is stochastically stable.