Dissipativity-Based Event-Triggered Sliding Mode Control of Discrete-Time 2-D Systems

This article focuses on dissipativity analysis and dissipativity-based sliding mode control (SMC) of discrete-time two-dimensional (2-D) systems described by Roesser model. First, dissipativity is introduced for 2-D systems. Aimed at the characteristics of Roesser model, the horizontal and vertical sliding surface functions are constructed for the addressed 2-D systems, respectively. Then, sufficient conditions are proposed to guarantee the asymptotic stability and the prespecified dissipativity for the resultant reduced-order 2-D sliding mode dynamics. Next, the SMC law is developed such that the system trajectories are driven into the quasi-sliding mode band in a finite region and maintained therein all the time. In order to achieve a better resource utilization, the event-triggered strategy is further incorporated in the design of SMC law. The event-triggered rule is also established to implement the event-triggered SMC scheme for 2-D systems. In the meantime, the corresponding quasi-sliding mode band is obtained. Finally, one verification example is given to show the effectiveness of the proposed SMC design method.