Robust sliding mode control for a class of uncertain linear 2-D discrete-time systems

For a class of uncertain linear two-dimensional (2-D) discrete-time systems, the problems of robust stability analysis, state feedback robust stabilization and robust sliding mode control is concerned. A sufficient condition is proposed for robust asymptotic stability of the autonomic system in terms of linear matrix inequality (LMI). Based on that condition, some sufficient conditions are also developed for the existence of stabilization controller and ideal sliding mode. Moreover, the reaching law method used for one-dimensional (1-D) discrete-time systems is further extended and improved to investigate the sliding mode controller (SMC) design for 2-D discrete-time system. A SMC is synthesized by using the extended reaching law method, which guarantees the closed-loop system robust and asymptotically stable. A numerical example illustrates the effectiveness of the proposed design scheme.