Event-triggered and self-triggered H∞ output tracking control for discrete-time linear parameter-varying systems with network-induced delays

In this paper, we address the event-triggered and self-triggered ${H_\infty } $H∞ output tracking problem of discrete LPV systems with network-induced delay. Considering the time delay and external disturbance, we formulate the closed-loop event-triggered output tracking problem into a time-delayed discrete polytopic linear parameter-varying system with relative event-triggering mechanism. Then, by constructing the parameter-dependent Lyapunov–Krasovskii functional, we derive a sufficient condition such that the closed-loop system is global asymptotic stable and satisfies the ${H_\infty } $H∞ output tracking performance. Further, we develop an approach to design the event-triggering mechanism and ${H_\infty } $H∞ output tracking controller. The parameters of event-triggering mechanism and the gains of output tracking controller are obtained by solving linear matrix inequalities. Moreover, we extend the results of the event-triggered control to the self-triggered ${H_\infty } $H∞ output tracking control. This not only mitigates the usage of network bandwidth but also avoids the use of additional hardware. Finally, the numerical simulation is included to illustrate the usefulness and effectiveness of the proposed approach.