Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
01 February 2020 |
16 February 2020 |
10 March 2020 |
Abstract: The problem of boundary stabilization is considered for a class of reactiondiffusion system with time delay. Semigroups have become important tools in infinitedimensional control theory over the past several decades. We show that the well known backstepping method proposed in the one dimensional case and for the undelayed system, still works well for a class of systems with time delay. The determination of the feedback controller require the solutions of some kernels equations, which are a system of coupled linear second-order hyperbolic equations which were recently founded to be well posed. Applying this result in our problem, allows us to prove an exponential stability for the closed loop system.
