Boundary Feedback Stabilization Of Reaction Diffusion Equations In Annular Region

This thesis addresses designs of inside boundary controller and outside bound-ary controller for reaction diffusion equations system in the annular region, which is one kind of distributed parameter systems. Lyapunov stability theory is employed to the research of the work. By constructing suitable Lyapunov functions(energy function) to design controllers and observers to achieve stability or stabilization of closed-loop systems.The main part of this thesis contributes to the control design of reaction dif-fusion equations systems in the annular region. When the state is independent of angle or height, the two dimensional equation system is transformed into one-dimensional by polar coordinate transformation or cylindrical coordinates transform. A Volterra transformation is introduced to convert the unstable system into an ex-ponentially stable system. Through backstepping technique to establish a controller which achieves exponential stabilization of the closed-loop system. In the process of design controller, one kernel function is generated. The kernel function satisfy a hy-perbolic partial differential equation (PDE), then the hyperbolic PDE is converted into equivalent integral equation. By the method of successive approximations, the well posedness of the kernel function is proved. Observer and output-feedback controller are designed according to the characteristics of the system when only boundary measurements are available. The exponential stabilization of the closed-loop system is proved. Beside, two examples were simulated to illustrate the design of the observer and the controller is feasible.