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This paper is concerned with the stochastic stability problem for discrete-time Markovian jump systems (DTMJSs) with time-varying delays. Two cases are discussed in the main results. On the one hand, it is assumed that the transition probability can be known. In this case, by constructing the Lyapunov-Krasovskii functional and using some summation inequalities to estimate its forward difference, a new stochastic stability criterion of DTMJSs can be obtained, which has less conservatism than existing results. On the other hand, by utilizing the homogeneous polynomial approach, the novel delay-dependent stability condition of DTMJSs with uncertain transition probability is proposed. Finally, the results of numerical simulations demonstrate the effectiveness of the proposed methods.

Stability Analysis for Discrete-Time Markovian Jump Systems With Time-Varying Delay: A Homogeneous Polynomial Approach