Stability Analysis Of Time-varying Time-delay Neural Networks

In recent years,neural network has been widely used in image processing,fault diagnosis,complex system control and other fields.It is well known that many applications of neural network systems are largely dependent on their dynamic behavior,especially for the existence and stability of equilibrium points.Moreover,due to the limited conversion speed and information processing speed of amplifiers in practical applications,time delay is often unavoidable in neural network systems.The existence of time delay not only reduces the performance of the system,but also leads to instability and even disorder of the system.In many practical problems,there is also a typical time delay different from the traditional time delay,called leakage delay,which is often ignored in many previous models.Generally speaking,the leakage delay tends to make the neural network unstable,so the leakage delay,like the traditional time delay,is the focus of current research.The main research work of this paper is as follows:Firstly,the stability of the neural network based on time-varying delay is analyzed,and the conservatism of the existing criterion is improved in two aspects.The first is to construct a reasonable Lyapunov–Krasovskii functional(LKF),and the second is to deal with the integral terms in the derivative of LKF by using an improved method.By combining these two methods,the stability criterion of time-varying delay neural network based on improved integral inequality is proposed,and its stability criterion is less conservative.Secondly,in order to further reduce the conservativeness,in order to analyze the stability of time-varying delay neural networks,the stability criterion of time-varying delay neural networks based on orthogonal polynomials and interactive convexity are proposed on the basis of the previous chapter to deal with the integral terms in the derivative of LKF.The stability criterion is improved compared with the previous chapter.Thirdly,the stability of the neural network with time-varying delay and leakage delay is analyzed.The influence of the leakage delay on the stability of the system is not negligible as the traditional delay.Therefore,in this chapter,a reasonable LKF is constructed for the system model,which contains more state information and time delay information.The integrals whose derivatives appear in LKF are treated by orthogonal polynomials and reciprocal convexity,and the stability criteria of neural networks with time-varying and leaky delays are obtained.Through the analysis of this chapter and the previous chapter,the influence degree of the leakage delay on the stability of the system is verified.Finally,the above methods are verified by combining different numerical simulation examples.Because the stability criterion obtained by LMI method is easy to be verified and compared by Matlab software toolbox LMI.Therefore,LKF and LMI are often used to analyze the stability of the system.Through numerical analysis results,the effectiveness of the method is proved and corresponding simulation is made.