Stability for discrete-time uncertain systems with infinite Markov jump and time-delay

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In this paper,we developed a stability analysis for discrete-time uncertain time-delay systems governed by an infinite-state Markov chain (DUTSs-IMC).Some sufficient conditions for the considered systems to be exponential stability in mean square with conditioning (ESMS-C) are derived via linear matrix inequalities (LMIs),which can be examined conveniently.Under novel sufficient conditions,the equivalence among asymptotical stability in mean square (ASMS),stochastic stability (SS),exponential stability in mean square (ESMS),and ESMS-C has been established.Besides,numerical simulations are employed in result validation.
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