Globally Asymptotic Stability Analysis Of Time-varying Delay Neural Network Based On LMI Approach

Neural network plays an important role in engineering fields, and the stability of neural network system occupy a very important position in the study of neural network system. So far many fruitful results have been obtained for stability of neural network with delay. It is well known that the delay in electronic implementation of neural networks is inevitable, the existence of time delay may cause instability and oscillation of neural networks. Now, many results about the stability of neural network are mostly try to expand the allowed maximum delay. In order to expand delay interval in the delayed neural networks, we often use some commonly methods and thechniques such as Lyapunov stability theory, the linear matrix inequality technique to reasonable and flexible reduce the conservative of the conclusions of the paper.In this paper, I mainly study the problem of delay-dependent asymptotic stability criteria for networks with time-varying delay, neural networks with discrete time-varying delay and distributed time-varying delay and BAM neural networks. The main works of this paper are sketched:The problem of delay-dependent asymptotic stability criterion for neural networks with time-varying delay is considered. In this, we are properly divide the delay interval, construct more appropriate function()tV y on the basis of the existing literature and use the linear matrix inequality technique to get the mainly conclusion. Finally, a numerical example is given to show the reliability of the novel criterion, and less conservative than some existing literature.The problem of delay-dependent asymptotic stability criterion for neural networks with discrete time-varying delay and distributed time-varying delay is considered. By dividing the delay interval into several unvariable and variable intervals, constructing different Lyapunov functional in these small intervals, and combining Schur lemma with LMIs approach to get the mainly conclusion in this chapter. Finally, a numerical example is given to show the rationality of the novel criterion, and less conservative than some existing literature.The problem of delay-dependent asymptotic stability criterion for BAM neural networks is considered, and a novel criterion is obtained by dividing delay interval into two small intervals, constructing different Lyapunov functional(,)i t tV x y in these intervals, and estabilishing several inequalities and equalities to deal with the upper bound of(,)t tV x y?. Finally, a numerical example is given to show the reliability of the novel criterion, and less conservative than some existing literature.