Stability Analysis Of Several Kinds Of Reaction-diffusion Systems

Reaction-diffusion stochastic differential equations have many important applications in the fields of chemistry,biology,physics and ecology.In addition,many real world systems with structural mutations,such as computer control systems,chemical processes,and the communications industry,can be effectively represented by Markovian jumping systems.Impulsive effects can be found in many fields such as physics,chemistry,population dynamics and optimal control,etc..As a kind of special nonlinear control,sliding mode control is widely applied to attenuating the parameters uncertainties of the system and external disturbances,for instance,robot manipulators,spacecrafts,fault-tolerant actuators,and so on.Therefore,the study of impulsive Markovian jumping stochastic reaction-diffusion system stability are of a certain practical background and theoretical significance.The main research contents of the paper are as follows:Firstly,by using Lyapunov-Krasovskii functional method and linear matrix inequalities,the global mean square exponential stability of Markovian jumping reaction-diffusion high-order Hopfield neural networks with uncertain transition rates is studied.The uncertain transition rate we consider is general,and the results obtained extend the results of previous studies and are less conservative.A numerical example is given to illustrate the validity of the conclusions.Secondly,by means of linear matrix inequalities,Lyapunov functional construction and Razumikhin technique,the sufficient conditions for robust mean square stability of impulsive time-varying delayed stochastic generalized uncertain reaction-diffusion cellular neural networks and uniform asymptotic stability of delayed impulsive reaction-diffusion systems are obtained.A simulation example is given to illustrate the feasibility of our findings.Thirdly,by using Lyapunov-Krasovskii functional method and linear matrix inequalities,several novel sufficient criteria on mean square exponential stability of Markovian switching stochastic neutral-type reaction-diffusion neural networks with time-varying delays are obtained.A simulation example is given to illustrate the feasibility of the conclusion.Finally,stabilization problem of a kind of impulsive uncertain systems with reactiondiffusion terms is studied by designing a sliding mode controller for reaction-diffusion impulsive uncertain systems.By means of linear matrix inequalities,the robustly exponentially stable of impulsive uncertain systems with reaction-diffusion terms are derived.Research results of sliding mode control theory for impulsive uncertain systems are extended.A simulation example is given to illustrate the rationality of the conclusion.