Finite Time Stability Of The Impulsive Stochastic Delay Systems With Applications

In the research of systems stability theory,the Lyapunov stability is often considered.That reflects the stable state performance of the systems,however in many practical applications,it is not enough to only focus on the stable state performance of the systems,and the transient performance of the systems also play an important role.The finite time stability exact describes the transient performance of the systems.Therefore,the problems of finite time stability attract a lot of scholars' attention.However,in these practical applications,the systems will inevitably be affected by the stochastic disturbances,impulse and time delay,which presence may become unstable and performance deteriorated for the systems.So,it is very important to study the finite time stability of impulsive stochastic systems with time delay.In this dissertation,Lyapunov functional method,average impulsive interval condition and linear matrix inequality are used to study the finite time stability of impulsive stochastic systems with time delay.This paper mainly includes the following aspects:1.In the introduction part,the significance and related research progress of impulsive stochastic systems with time delay are introduced.2.The finite time stability of linear impulsive stochastic systems with time delay and uncertain linear impulsive stochastic systems with time delay are studied.By constructing a suitable Lyapunov functional,and combining with stochastic analysis techniques?the average impulsive interval condition and linear matrix inequalities tool,we obtain the theorems of the mean square finite time stability.Based on the study of stability,the design strategy of state feedback controller is given.3.Under the previous study of linear systems,the sufficient conditions for the finite time stability of general impulsive stochastic systems with time delay are given.Three types of impulsive are discussed: the impulses are stabilizing,the impulses are input disturbances and the impulses are neutral type.4.The finite-time stability of a class of impulsive stochastic neural networks with time delay is studied.By constructing a suitable Lyapunov functional,combining with the average impulsive interval condition and linear matrix inequality tool,the sufficient conditions for the finite-time mean square stability of neural networks are established for different impulses.Finally,a numerical example of uncertain impulsive stochastic neural networks with time delay is given to verify the effectiveness of the theoretical results.Finally,the conclusions and some issues are proposed in the future.