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.

中文翻译：

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具有无限马尔可夫跳跃和时滞的离散时间不确定系统的稳定性

在本文中，我们开发了由无限状态马尔可夫链（DUTSs-IMC）控制的离散时间不确定时滞系统的稳定性分析。通过线性矩阵不等式（LMI）可以得出考虑的系统具有均方根条件下的指数稳定性（ESMS-C）的一些充分条件，可以方便地对其进行检查。在新颖的充分条件下，均方根的渐近稳定性（ASMS），随机稳定性（SS），均方指数稳定性（ESMS）和ESMS-C之间的等价关系已经建立。此外，数值模拟用于结果验证。