Exponential Stability Analysis Of Stochastic Hybrid Systems With Time Delay

Stochastic hybrid system is a kind of complex system formed by the combination of stochastic system and hybrid system,which is extensively applied in many important fields such as economics,control science,biological science,neural network and so on.In recent years,stochastic hybrid system has been widely concerned by many scholars at home and abroad.Stability,as the primary consideration problem in the study of practical systems,especially the exponential stability of systems,which has always been a hot research topic.In practical systems,time-delay,uncertain parameters,stochastic disturbances and other factors have a great impact on the stability of the system.Therefore,it has important significance both in theory and application to study the influence of these factors on the stability of the system.Based on the existing research,this paper mainly discusses the exponential stability problems of stochastic switch hybrid system,stochastic impulsive hybrid system and uncertain stochastic hybrid system under the influence of time delay.The main research contents of this paper are as follows:Firstly,for the stability problem of switched stochastic hybrid systems under the influence of time delay,the P-order exponential stability and the mean square exponential stability theorem of the system are obtained by combining the Lyapunov function with the average dwell time and constructing the quadratic function method.Numerical simulations show that the combination of average dwell time and Lyapunov function can improve the convergence rate.Secondly,for the stability of the system under the action of impulses,by the idea of impulse control,the exponential stability of impulsive stochastic hybrid systems with time-delay is studied.By constructing a suitable multi-Lyapunov function method,using the relevant integral transformation and inequality techniques,and by stochastic analysis techniques and Schur complement lemma,the sufficient conditions for the stability of the system are derived.Through simulation analysis,it is found that the system can not reach a stable state quickly without impulse,but it can reach a stable state quickly under impulse.Comparing the obtained stability results with the existing literatures,the results of this paper are less conservative.Finally,based on the above research,the exponential stability of stochastic hybrid systems with uncertain parameters under the influence of time delay is discussed.By constructing a suitable Lyapunov function,the exponential stability discriminant theorem of the system is obtained by using the integral inequality method and the linear matrix inequality technique.The correctness of the theoretical analysis is verified by simulation analysis of specific examples.