Robust sliding mode control for uncertain discrete singular systems with time-varying delays and external disturbances

In this paper, a sliding mode control (SMC) of uncertain discrete singular systems with external disturbances and time-varying delays is under consideration. By use of the free weighting matrices and the Lyapunov–Krasovskii functional, a delay-dependent sufficient condition is given in strict linear matrix inequality (LMI) format to guarantee the sliding mode dynamics to be admissible (regular, causal and stable). Furthermore, a proposed SMC law and an adaptive SMC law are synthesized to make sure that the trajectories of system can be driven to a region near equilibrium point in finite time. Finally, a numerical example is designed to display the effectiveness of the control scheme. All these results are expected to propose a new approach for the research on SMC of discrete time-delay singular systems.