Stability And Application Of Neutral Stochastic Systems With Proportional Delay And Markov Switching

In practice,due to the interference of the external environment and the existence of mutation,the stochastic Markov switching system can more accurately simulate this kind of phenomenon.In addition,proportional delay,as a special kind of unbounded delay,will have an important impact on the performance of the system.At present,Markov switching systems with neutral proportional delay have been widely used in various fields,such as mechanical engineering,biological systems,control engineering and neural network systems.It is of great theoretical significance to analyze their dynamic behavior and control problems.In this paper,we mainly study the stability of neutral stochastic proportional delay systems with Markov switching(NSPSMS)and their applications in neural network systems.The details are as follows.The first chapter mainly introduces the research background and significance of neutral stochastic proportional delay systems,the research status,and the main research content of this paper.In Chapter 2,we set up the stochastic LaSalle theorem to locate the attractive sets for NSPSMS without linear growth conditions.Subsequently,combining the stochastic LaSalle theorem and uniformly continuous theory,almost surely asymptotic stability and pth moment asymptotic stability are analyzed.Furthermore,we also present one new criterion on the pth moment polynomial stability and almost surely polynomial stability for NSPSMS,where the coefficients of the delay term are time-invariable.Then,three examples are provided to exhibit the efficiency of the proposed results.Finally,the numerical simulations are carried out.In Chapter 3,by adopting the Razumikhin approach,one new criterion on the moment polynomial stability of NSPSMS is established.Moreover,combining with the Chebyshev inequality and the Borel-Cantelli lemma,the almost sure polynomial stability of NSPDEs MS is examined.Finally,two examples are provided to illustrate the effectiveness of the theoretical work.In Chapter 4,the obtained theory in Chapter 2 is applied to the neutral stochastic neural network system with proportional delay and Markov switching,and the moment stability and almost sure polynomial stability are investigated.The fifth chapter summarizes the research content and points out the direction of future improvement and further research.The work of this paper not only enriches and develops the dynamic theory of stochastic unbounded delay systems,but also provides a theoretical premise for the application of such systems in practice.