A Descriptor System Approach to Discrete-Time Sliding Mode Control for Uncertain Systems with Time-Varying Delays

This paper investigates the descriptor system approach to discrete-time sliding mode control (DT-SMC) design for uncertain linear systems with time-varying delays. By applying a descriptor model transformation and Moon´s inequality for bounding cross terms, a delay-dependent sufficient condition for the existence of stable sliding surface is given in terms of linear matrix inequalities (LMIs). Based on this existence condition, the synthesized sliding mode controller can guarantee the sliding-mode reaching condition of the specified discrete-time sliding surface for all admissible uncertainties and time-varying delays. An illustrative example verifies the effectiveness of the proposed method.