Robust stability analysis of discrete-time systems depending on Markov processes

Abstract

In this paper, we deal with discrete-time stochastic systems whose state transition is determined with time-varying random matrices depending on Markov processes. We first consider the case where the Markov processes (i.e., the associated random matrices) underlying systems include no uncertainties, and show a linear-matrix-inequality-based stability condition for the systems, through the use of conditional expectation. Then, we further consider the case where the systems are uncertain in the sense that they are characterized by random polytopes with some deterministic uncertain time-invariant parameters, and extend the result about the above uncertainty-free case toward robust stability analysis.