Sliding mode control to stabilization of the coupled PDE-PDE system with boundary input disturbance

Abstract

This paper is about the stability analysis of the coupled partial differential equation(PDE)-PDE system with boundary input disturbance. The sliding mode control(SMC) and backstepping control(BC) approach are combined to cope with the boundary disturbance, which is supposed to be bounded. An infinite-dimensional sliding surface is constructed by Lyapunov method and the exponentially stability is proved in spite of accompanying with the boundary input disturbance. The variable structure boundary controller is designed to stabilize the unstable system. At last the availability of this approach is illustrated by some numerical simulations.