Exponential stability and robust \(H_\infty\) control for discrete-time time-delay infinite Markov jump systems (Q1727074)

Summary: In this paper, exponential stability and robust \(H_{\infty}\) control problem are investigated for a class of discrete-time time-delay stochastic systems with infinite Markov jump and multiplicative noises. The jumping parameters are modeled as an infinite-state Markov chain. By using a novel Lyapunov-Krasovskii functional, a new sufficient condition in terms of matrix inequalities is derived to guarantee the mean square exponential stability of the equilibrium point. Then some sufficient conditions for the existence of feedback controller are presented to guarantee that the resulting closed-loop system has mean square exponential stability for the zero exogenous disturbance and satisfies a prescribed \(H_{\infty}\) performance level. Numerical simulations are exploited to validate the applicability of developed theoretical results.