Stability Of Neural Networks With Impulses And Time-varying Delays

In this paper,Lyapunov functional method,matrix inequality and the mathematical induction are used to study several kinds of neural networks with impulses and time-varying delays.We obtain the sufficient conditions for the stability of equilibrium solution,improve and generalize the results of the relevant literature.This thesis is consists of four chapters.In Chapter 1,the historical development,research status of neural networks and the main research contents of this paper are introduced.In Chapter 2,the exponential stability of neural networks with impulses and time-varying delays is studied.In this chapter,impulsive perturbation is considered on the basis of existing model.The exponential stability of neural networks is proved by constructing a simpler Lyapunov function,and an example is given to illustrate the effectiveness of the results.In Chapter 3,the -stability of inertial neural networks with impulses and time-varying delays is studied.The most majority of previous studies considered the first derivative of the neural networks but ignored the influence of inertial term.In this chapter,we prove the -stability of inertial neural networks by using Lyapunov functional method and the mathematical induction,improve the assumption of the relevant literature,and give examples to illustrate the effectiveness of the results.In Chapter 4,the global exponential stability of inertial neural networks with impulses and distributed delays is studied.In this chapter,we prove the global exponential stability of inertial neural networks by using Lyapunov functional method,matrix inequality and the mathematical induction,generalize the model of relevant literature and improve assumption of the model,and give examples to illustrate the effectiveness of the results.