Event-triggered sliding mode control for discrete-time singular system

This study focuses on the discrete-time sliding mode control (SMC) based on event-triggered approach for discrete-time singular system. The purpose is to design a SMC law under event-triggered to ensure that the discrete-time singular system is admissible. A novel event-triggered sliding mode surface is constructed, and a sufficient condition, in the form of linear matrix inequality (LMI), is investigated to guarantee the admissibility of the discrete-time singular system. One can verify this condition by utilising the toolbox YALMIP of MATLAB. In addition, the expected controller gain matrix can be represented by a feasible solution of LMI. Then, based on the above solved sliding mode controller gain, a new discrete-time event-triggered SMC law is constructed to ensure that the discrete-time singular system can be driven onto the sliding surface in finite time and then is maintained there for all subsequent time. Finally, three examples are presented to illustrate the effectiveness of the theoretical results.