Periodic event-triggered state-feedback control for discrete-time linear systems

Abstract

This paper investigates the periodic event-triggered control for discrete-time linear systems. The discrete-time plant denotes a combination of the continuous-time controlled plant, the sensors and the actuator. A general packaged component, event machine, is introduced to conduct the detection and judgement of the events. Then the periodic event-triggered control for the discrete-time system including a discrete-time plant, an event machine, a transmitter and a continuous static controller, exhibits some different behaviors from that for the continuous-time system. Especially, in this system, the sampling sequences and the event-verifying sequences may be independent from each other. Furthermore, according to the difference between the two sequences, the periodic event-triggered control system is classified into three cases, and the corresponding models are established for the three cases: a discrete-time perturbed linear system, a discrete time-delay system and a switched system, respectively. Moreover, the stability conditions for the three cases are proposed. Finally, a numerical example is given to illustrate the efficiency and feasibility of the obtained results.