Exponential Stability Of The Mixed Varying Delay Neural Network Analysis

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 exponential stability for several neural networks with mixed time-varying delays.More specifically,the main contributions are as follows:1)Delay-dependent exponential stability criterion for uncertain stochastic neural networks with mixed time-varying delays.A new method is proposed to study the exponential stability for a class of uncertain stochastic neural networks with mixed time-varying delays.By constructing a new Lyapunov-Krasovskii function,free-weighting-matrix method is utilized to establish sufficient conditions ensuring the system to have a globally exponentially 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 those of the present literatures.2)Delay-dependent exponential stability criterion of neural networks with mixed timevarying delays.Based on Lyapunov stability theory and linear matrix inequality technique,an integral inequality approach and free-weighting-matrix method are utilized to derive the delay-dependent robust stability condition for a class of neural networks with mixed time-varying delays.The proposed stability criterion can be checked by the Matlab LMI Control tool-Toolbox. Finally,the effectiveness of the result is demonstrated by an example.