Discrete sliding-mode control of uncertain systems with time delays

Robust problem is researched for the discrete-sliding-mode control (D-SMC) design for a class of uncertain linear systems with time-varying delays. By using a descriptor model transformation and Moons inequality for bounding cross terms, a delay-dependent sufficient condition for the existence of stable sliding surface is given by means of linear matrix inequalities (LMI). 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 multiple state delays. An illustrative example verifies the effectiveness of the proposed method.