Boundary Control Of Stochastic Delay Reaction-diffusion Systems With Markovian Switching

Stochastic reaction-diffusion systems have wide applications in physics,biology,chemistry and other fields.When the system structure changes suddenly,a continuoustime Markov chain orchestrates the switching process between operation modes.In many cases,time delay is unavoidable and may result in uncertain performance.To achieve the desired asymptotic stability and even finite-time stability,various distributed control methods have become a hot research subject.However,it requires the actuators to be distributed everywhere in the spatial domain,which has some limitations in practical application.Based on the spatial distribution characteristics of partial differential systems,the stabilization problem of stochastic delay reaction-diffusion systems with Markovian switching is studied via boundary control strategy.In addition,when the uncertain external disturbance enters the system,H-infinity index is an effective indicator to measure the impact of external disturbance on the system state.It is also of great significance to investigate the H-infinite boundary control issue.Chapter 2 deals with the mean square asymptotic stabilization for stochastic Markovian reaction-diffusion systems with time delay.Firstly,a mode-dependent boundary controller is designed.By Lyapunov-Krasovskii functional and Poincaré inequality,a sufficient criterion of mean square asymptotic stability is established for the system with constant time delay.Next,asymptotic stabilization for the system with timevarying delays is also investigated,and a delay-dependent sufficient condition is obtained.For the system with parametric uncertainty,the robust boundary stabilization is considered.Chapter 3 investigates the problem of finite-time stabilization for stochastic delay reaction-diffusion systems with Markovian switching.We first consider the case without delay.Based on the finite-time stability lemma of stochastic systems,a sufficient condition to ensure finite-time stability in probability is derived under the designed boundary control law.The finite time boundary controller of the system with time delay is further designed,and then the finite-time stability condition is obtained.In Chapter 4,H-infinity control of stochastic delay reaction-diffusion systems with Markovian switching is studied.H-infinity boundary controller is presented for the system with external disturbance.Using Lyapunov functional method and stochastic analysis technique,a sufficient condition is provided to achieve H-infinity performance in the mean square sense.Each chapter also ends with numerical examples to illustrate the validity of the derived results.At last,a brief summation is presented for our research and some work is put forward to be further studied.