$H_{\infty}$ Control for Singular Markovian Jump Delay Systems with Mode-Dependent Derivative-Term Coefficient

Abstract

This paper focuses on the $H_{\infty}$ control problem of singular Markovian jump delay systems with mode-dependent derivative-term coefficient through an extended decomposition system. By computing a proper Lyapunov functional, a generally stochastic stability condition of singular Markovian jump systems is achieved. On this basis, a delay-dependent stabilization condition of considered system is derived in terms of tractable linear matrix inequalities (LMIs), and the $H_{\infty}$ controller gains are directly designed. Two numerical examples are introduced to illustrate the effectiveness of the proposed results.