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This paper introduces sufficient Lyapunov conditions guaranteeing exponentialmean square stability of discrete-time systems with markovian delays. Weprovide a transformation of the discrete-time system with markovian delays intoa discrete-time Markov jump system. Then, we extend sufficient Lyapunovconditions existing for the global asymptotic stability of discrete-timesystems with delays digraphs to the mean square stability of discrete-timesystems with markovian delays. Finally, an example is provided to illustratethe efficiency and advantage of the proposed method.

Sufficient Lyapunov conditions for exponential mean square stability of discrete-time systems with markovian delays (extended version)