$H_{\infty}$ sliding mode control problem for uncertain singular Markovian jump system with time-varying delays

In this paper, we deal with the $H_{\infty}$ sliding mode control (SMC) problem for uncertain singular Markovian jump systems with time-varying delays. First, an integral-type switching surface function is constructed. Then, by using a Lyapunov Krasovskii functional which depends on time delays and system modes, we obtain the sufficient conditions for stochastic admissibility of sliding mode dynamics with a given disturbance attenuation level which are expressed in terms of strict linear matrix inequalities (LMIs). Moreover, a SMC law is designed to ensure that system states can reach the predefined sliding surface finally. Finally, a numerical example is given to show the effectiveness of the proposed method.