Abstract

This paper considers the global sliding mode control (GSMC) technique based on linear matrix inequality (LMI) approach for uncertain discrete-time descriptor systems with multiple time-varying delays. Using some free-weighting matrices and the Lyapunov-Krasovskii functional, the strict LMI conditions are established to ensure that the closed-loop dynamics are admissible, i.e., regular, causal and stable. Based on the Lyapunov stability theorem and LMI constraint, the sufficient condition for the asymptotic stability of the sliding mode dynamics is obtained. A new control law is designed to guarantee the elimination of the reaching mode, and then satisfy the robust performance of the closed-loop system against parametric uncertainties and time-delays. The global sliding surface provides the robust performance by the removal of the reaching phase, causes reduction of the control effort, and forms sliding around the surface right from the beginning. Finally, a numerical example is presented to confirm the validity of the proposed method.