| Hyperbolic systems are widespread in many life and engineering situations.In recent years,the control problem of the hyperbolic systems has drawn attention of many scholars to conduct advanced research.In this thesis,boundary stabilization of first-order linear integro-differential hyperbolic partial differential equation(PIDE)is studied by means of proportional-integral(PI)control.The main results of this thesis are as follows:1.A weighted Lyapunov function is constructed,which gives a sufficient condition for exponential stability of closed-loop systems.Since this suficient condition is in matrix inequality form,it is numerically manageable when looking for PI controller.2.Applying the result of the first part,the suficient condition for the firstorder hyperbolic systems to achieve exponential stability by PI controller is also discussed in different situations.In particular,the sufficient condition is explicit.The difficulties in this thesis exist in two aspects.On the one hand,the Lyapunov function required in the proof is of various forms,so how to construct a suitable Lyapunov function candidate with PI boundary control is the critical challenging problem of this thesis,which requires numerous attempts;On the other hand,due to the non-local term of the system,the derivative of the Lyapunov function needs specific processing,which brings new difficulties to the relevant research. |
