$H_{\infty}$ Controller Design for Discrete-Time Markovian Jump Systems with Additive Time-Varying Delays

This paper focuses on the H
_∞
controller design problem for discrete-time Markovian jump systems with additive time-varying delays. By combining Lyapunov-Krasovskii functional approach and Wirtinger-based inequality, a sufficient condition is established such that the resulting closed-loop system is stochastically stable with a prescribed H
_∞
performance level γ. Then, by employing the singular value decomposition technique, the controller gains are given by using feasible solutions to a certain set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the usefulness of the scheme developed in this paper.