Stability, Stabilization And Control Of Stochastic Reaction Diffusion Systems

An approach is designed to study stability, stabilization and control problem of stochastic systems with reaction-diffusions. The approach is based on Lyapunov direct method. Employing this approach, the basic theory of stability is established for stochastic systems with reaction-diffusions.It is well known that it is similar to study stability of stochastic ordinary differential systems and determinate ordinary differential systems by using Lyapunov direct method. The derivative V(t,x(t)) of the V function along a solution to a determinate ordinary differential system is changed to be LV(t,x(t)) for a stochastic ordinary differential system. However, since there is no Ito formula for stochastic partial differential systems, now the methods to deal with this problem can be categorized as: one is to analyze every behavior of the solutions to the systems; two is to analyze the properties of the solution processes by using semi-group theory in an abstract space. In this paper, our idea is based on " integral the solution process to the systems, and view the integration as a solution process to the corresponding stochastic ordinary system ". By constructing a mean Lyapunov function with respect to the space variables and using Ito formula under the integral operators, we directly study stability, stabilization and control problem of stochastic systems with reaction-diffusions. Thus, we bypass the difficulty of lacking It6 formula for stochastic partial systems.This dissertation is composed of eight chapters:1 Expatiate the significance of studying stochastic systems and the status in quo of the study. Then we show the main idea and entire structure of this dissertation.2 To write a self-contained dissertation, we simply discuss dissipation, stability of reaction-diffusion systems with random coefficients. And some concepts are presented.Properties of It6 type stochastic systems with reaction-diffusions are discussed in Chapter 3—8. Some constants are included3 Based on theory of differential systems, employing iteration method and martingale inequality, the existence and uniqueness of mixed problem are proved for stochastic systems with reaction-diffusions.4 The Lyapunov basic theory of stochastic systems with reaction-diffusions is...