Almost sure stability of stochastic linear systems with ergodic parameters: an average contractivity criterion

This paper deals with the notion of almost sure stability for linear stochastic systems whose dynamic matrix depends on an ergodic process. It is shown that such systems are exponentially almost surely stable if and only if their transition matrix is averagely contractive over a finite, yet unknown, time interval. In order to test almost sure stability, an efficient computational procedure based on a Monte Carlo strategy is proposed. The applicability of the proposed method is illustrated by means of a numerical example