Handling Asynchronous Scheduling Functions in Periodic Event-Triggered Gain-Scheduled Control With Guaranteed Polytopic Inclusion

This article deals with periodic event-triggered control (PETC) of nonlinear systems, considering an equivalent quasi-linear parameter-varying (quasi-LPV) polytopic representation of the nonlinear plant and a gain-scheduled controller for stabilization. Although gain-scheduling approaches allow one to improve the results and extend the set of feasible solutions to the co-design problem, the event-based sampling induces the so-called asynchronous scheduling functions, which void the gain-scheduling advantages, leading to conservative results, especially in the PETC framework. The dominant approaches for dealing with this issue consider a bounding assumption on the mismatched scheduling functions, but do not guarantee that those bounds cannot be violated during the closed-loop operation. To properly manage the asynchronous phenomenon, we propose a novel PETC scheme. Based on the looped-functional approach and a nonquadratic Lyapunov function, we derive linear matrix inequality (LMI)-based conditions to co-design the event-triggering mechanism and the gain-scheduled controller. These conditions are incorporated into a multiobjective optimization problem to maximize the estimate of the region of attraction of the origin and minimize the number of transmissions of the PETC scheme. We prove that the closed-loop trajectories initiated in the estimated region of attraction converge toward the origin without violating the boundedness of the mismatched scheduling functions during operation. Two numerical examples are provided to illustrate the methodology.