Robust stability analysis of discrete-time linear systems characterized by stochastic polytopes

This paper discusses robust stability analysis of discrete-time stochastic systems whose system matrices belong to convex polytopes (called stochastic polytopes) consisting of random matrices (i.e., matrices involving random variables). The stochastic polytopes enable us to describe the uncertainty in the probability distribution of the system matrix. Hence, we can tackle the problem of deciding whether the system is robustly stable (in the stochastic sense) with respect to the uncertainty in the distribution, through dealing with the stochastic polytopes. This paper gives sufficient conditions for analyzing such robust stability, and provides a numerical example showing the effectiveness of the developed analysis framework.