Accumulative-Error-Based Event-Triggered Control for Discrete-Time Linear Systems: A Discrete-Time Looped Functional Method

This paper is concerned with event-triggered control of discrete-time systems with or without input saturation. First, an accumulative-error-based event-triggered scheme is devised for control updates. When the accumulated error between the current state and the latest control update exceeds a certain threshold, an event is triggered. Such a scheme can ensure the event-generator works at a relatively low rate rather than falls into hibernation especially after the system steps into its steady state. Second, the looped functional method for continuous-time systems is extended to discrete-time systems. By introducing an innovative looped functional that links the event-triggered scheme, some sufficient conditions for the co-design of control gain and event-triggered parameters are obtained in terms of linear matrix inequalities with a couple of tuning parameters. Then, the proposed method is applied to discrete-time systems with input saturation. As a result, both suitable control gains and event-triggered parameters are also co-designed to ensure the system trajectories converge to the region of attraction. Finally, an unstable reactor system and an inverted pendulum system are given to show the effectiveness of the proposed method.