Robust Stability Analysis of Discrete-Time Linear Systems with Dynamics Determined by a Markov Process

Abstract In this paper, we deal with discrete-time linear stochastic systems whose state transition is described by a sequence of random matrices determined by a Markov process. For such systems, we first show a linear-matrix-inequality-based stability condition. The use of conditional expectation plays a key role in the derivation. Then, we assume that the systems are uncertain in the sense that they are described by a sequence of random polytopes determined by a Markov process (to which the actual underlying random matrix sequence should belong), and extend the result about the above uncertainty-free case toward robust stability analysis, which leads to our main result. To show the usefulness of the result, we apply it to the case with stochastic switched systems having uncertain coefficient matrices, and provide a numerical example.