Asymptotic Stability Of Delayed Cellular Neural Network Model Study

The delayed neural networks exhibiting the rich and colorful dynamical behaviors are important part of the delayed neural systems. Due to their important and potential applications in signal processing, image processing, artificial intelligence as well as optimizing problems and so on, the dynamical issues of delayed neural networks have attracted worldwide attention in recent years. Recently, many interesting stability criteria (such as asymptotic stability, complete stability, absolute stability, and exponential stability) for the equilibriums of delayed neural networks have been derived via Lyapunov-type functional approaches. This thesis mainly focuses on the global asymptotic stability for several delayed neural networks. More specifically, the main contributions are as follows:1) Delay-dependent asymptotic stability criterion of neural networks with time-varying delays.A new method is proposed to study the delay-dependent asymptotic stability for a class of neural networks with time variable delays. By constructing a new Lyapunov-Krasovskii function, a integral inequality approach is utilized to establish sufficient conditions ensuring the system to have a unique, globally asymptotically stable equilibrium point. This condition is expressed in terms of linear matrix inequality form that can be readily checked by the Matlab LMI Toolbox. Examples illustrate that the new results are less conservative than that of the present literatures.2)Delay-dependent robust stability criterion of neural networks with time-varying delays.Based on Lyapunov stability theory and linear matrix inequality, delay-dependent robust stability is derived for a class of neural networks with time-varying delays and norm-bounded uncertainties. The result is obtained under mild conditions, assuming neither differentiability nor monotonicity for activation function. And the restriction of the derivative of the time-varying delay is removed. The proposed stability criterion can be checked by the LMI Control Toolbox in Matlab. Finally, the effectiveness of the result is demonstrated by a example.3) Novel results concerning delay-dependent asymptotic stability of delayed cellular neural networks.Based on the Lyapunov stability theory and free-weighting-matrix method, delay-dependent asymptotic stability is concentrated upon for a class of neural networks with time-varying delays. This criterion can be applied to the case that the derivative of a time-varying delay is more than 1, and it is less conservative than that of the present literatures. The effectiveness of the result is demonstrated by examples.