Co-design of event-triggered H∞ control for discrete-time linear parameter-varying systems with network-induced delays

The additional threshold of a mixed event-triggering mechanism makes it impossible to guarantee the requirement of asymptotic stability. As a consequence, it is necessary to investigate uniform ultimate boundedness which is a mild stability property. In this paper, we address event-triggered H∞ control for discrete-time linear parameter-varying systems by jointly designing a mixed event-triggering mechanism and a set of state feedback controllers. In the frame of time-delay system, we propose a parameter-dependent sufficient condition such that the closed-loop system with mixed event-triggering mechanism is globally uniformly ultimately bounded with a minimized ultimate bound for a certain disturbance attenuation level. As an extensive study, such sufficient condition is proved to be in a sense of global asymptotic stability when the additional threshold tends to zero. To avoid the infinite dimensional optimization problem, the proposed parameter-dependent co-design condition is relaxed as a finite set of linear matrix inequalities at the polytope vertices, which can be numerically trackable and computationally efficient. Two numerical examples are provided to demonstrate the effectiveness of the proposed method.