Stabilization of a heat equation with an integral type boundary condition

Abstract

This paper considers the stabilization of a heat equation with an integral type nonlocal boundary condition. Via choosing a new intermediate target control system with undetermined term instead of the determined one appeared in the normal backstepping method, we convert the original control system into the intermediate target control system by backstepping transformation. At the same time, we prove the exponential stabilization of the intermediate target control system by Lyapunov function method after choosing an appropriate linear integral feedback control. Then, combined with the invertibility and boundedness of backstepping transformation, we obtain the exponential stability of closed-loop system. Finally, the simulation shows the validity of the main theorem.