Feedback Stabilization Of The Wave Equations And Kirchhoff Beam Equation

Feedback stabilization is an important content in the field of distributed parameter con-trol systems.The feedback stabilization means to design the controller according to the state of the system in order that the system under such a control can keep some stability The thesis study the feedback control problem of a wave system coupled and the feedback stabilization of a Kirchhoff beam system.The thesis is arranged as follows.In Chapter 1,we show some introduction on the feedback stabilization of the controlled system modeled by Partial differential equation(PDE).In Chapter 2,the boundary state feedback control problem of the wave equations cou-pled by displacement is considered:The boundary state feedback control assumed to have an input saturation constraint.First,an auxiliary system is introduced to eliminate the influence of input saturation constraint.The boundary feedback controller is designed based on the method of Lyapunov function and the exponential stability of the closed-loop system is proved.Besides,the existence and the uniqueness of the closed-loop system solution is proved by Galerkin method.In Chapter 3,the boundary feedback stabilization of the following Kirchhoff beam is studied:where the nonlinear function F(·)satisfies some conditions.The boundary state feedback controller is designed based on a integral Lyapunov function.The exponential stability of the closed-loop system is proved.Besides,the existence and the uniqueness of the closed-loop system solution is proved by Galerkin method.