Boundary Control Of Stochastic Reaction Diffusion Systems With Markovian Switching

In the real life,stochastic reaction-diffusion systems can be used to describe natural phenomena in many fields such as biological population,neural networks.In addition,if the system is subject to structural changes or environmental disturbances,it can be characterized by the Markov system.For a long time,the stability of the system has always been a hot topic.When the system cannot reach stability by itself,the stability can be achieved by adopting a controller.Because of its low cost and simple operation,boundary control has become an important control strategy for system to achieve stability.This paper will use full-domain control and boundary control to study the mean square asymptotical stabilization and mean square H-infinity control for two kinds of stochastic reaction-diffusion systems with Markovian switching.In chapter 2,under the condition that the transition probability is known,we study the mean square asymptotical stabilization and mean square H-infinity control for stochastic reaction-diffusion systems with Markovian switching.The full-domain controller and boundary controller are applied to the stochastic reaction-diffusion systems with Markovian switching respectively,the sufficient conditions for the systems to achieve mean square asymptotical stability are given by virtue of Lyapunov functional method,M-matrix theory and linear matrix inequality techniques.When the considered system is disturbed by external additive noise,full-domain controller and boundary controller are designed and the sufficient conditions for the systems to achieve mean square H-infinity performance are obtained.In chapter 3,under the condition that the transition probability is partially known,we investigate the mean square asymptotical stabilization and mean square H-infinity control for stochastic reaction-diffusion systems with Markovian switching.For the asymptotical stabilization in the mean square,under the full-domain controller and boundary controller,we obtain sufficient conditions for the stochastic reaction-diffusion systems with Markovian switching to achieve mean square asymptotical stability by constructing appropriate Lyapunov-Krasovskii functional.When the system is subjected to external disturbances,sufficient conditions are got for stochastic reaction-diffusion systems with Markovian switching to achieve mean square H-infinity performance.In addition,numerical examples are given to verify the validity of the obtained theory at each end of chapters.