On almost sure stability of discrete-time Markov jump linear systems

In this paper, we study the almost sure stability of discrete-time jump linear systems with a finite-state Markov form process. New sufficient conditions for almost sure stability are derived via the definition of a lifted representation of the Markov chain. These conditions depend on an integer parameter m, the length of the lifting horizon. It is shown that, if the system is exponentially almost sure stable, there exists a finite m such that the new criterion is satisfied. Since for large values of m the exact evaluation of the condition may become computationally prohibitive, an efficient Monte Carlo algorithm is worked out.