Asymptotic Mean-Square Stabilization for Mean-Field Stochastic Markov Jump System with Multiple Delays

In this paper, the operator spectrum theory is applied to study the asymptotic mean-square stabilization for discrete-time mean-field stochastic Markov jump systems (MF-SMJSs) with multiple delays. First, we adopt a feasible model augmented strategy to equivalently transform the considered stochastic dynamics into an auxiliary delay-free model. Then, by utilizing a delay-dependent linear Lyapunov operator (DDLLO), we construct two sets of stabilizing conditions: Lyapunov type and spectrum type. It is remarkable that the developed conditions are both necessary and sufficient, which can be verified availably by LMI feasibility tests. To confirm the effectiveness of our theoretic results, an illustrative example is included.