Event-triggered boundary stabilization for coupled semilinear reaction–diffusion systems with spatially varying coefficients

Abstract

This paper aims to address the event-triggered Robin boundary control problem for exponential stabilization of the coupled semilinear reaction–diffusion systems with spatially varying coefficients. The main used method is the backstepping, which allows us to explicitly give the boundary control formulae. More precisely, we first explore the existence and uniqueness of classical solutions for the considered problem. After this, we propose an event-triggered boundary feedback control law to exponentially stabilize the system under consideration with the Zeno phenomenon being excluded. A numerical result is finally included to illustrate the efficiency of our designed controller.