Exponential stabilization using sliding mode control for singular systems with time-varying delays and nonlinear perturbations

This paper considers a sliding mode control (SMC) of singular systems. The systems under consideration involve nonlinear perturbations and time-varying delays. The aim of this paper is to design a sliding mode controller such that the nonlinear singular system is exponentially stable and its trajectory can be driven onto the sliding surface in finite time. By using the Lyapunov–Krasovskii functional and some specified matrices, conditions on exponential stabilization are obtained in the form of strict linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed main results. All these results are expected to be of use in the study of singular time-varying delay systems with nonlinear perturbations.

Research highlights
► Sliding mode control for singular systems with time-varying delays are studied.
► Lemmas are developed which will help in the discussion of exponential stability.
► Novel conditions on exponential stabilization are developed.
► The results have the potential to be useful for the study of singular systems.