Study On Global Exponential Stability Of Several Kinds Of Cellular Neural Networks

Cellular neural network is an information processing system.Its characteristic is local connections between cells,and its output functions are piecewise linear.So,it is easy to realize large-scale nonlinear analog signals in real time and parallel processing,which improves the running speed.Cellular neural network has been applied to many fields,such as,the optimization,pattern recognition and image processing.Stability is the premise that cellular neural network is applied to practical problems.Because the switching speed of amplifier is limited and the errors occur in electronic components,time delays happen to neural network,and the time delays often destroy the stability of cellular neural networks system,even cause the system to produce heavy oscillation.It has great theoretical value and practical significance to research the stability of delayed cellular neural networks.By nonlinear measure method,this thesis mainly discusses global exponential stability of some categories of cellular neural networks with time delays.The detailed research contents are as follows:1.We study global exponential stability of cellular neural networks with multi-proportional delays.By means of study on stability of differential inequality with unbounded delays,and then we use the results obtained and nonlinear measure method,the sufficient condition to global exponential stability of the network is obtained.2.We research global exponential stability of periodic cellular neural networks with time-varying delays.By nonlinear measure method and to promote Halanay inequality,we enjoy a sufficient condition to global exponential stability of the networks.3.Global exponential stability of cellular neural networks with distributed delays is dealt with.The stability condition of a class of differential inequalities with distributed delays is acquired.Combined with the condition and nonlinear measure method,global exponential stability condition of the networks is obtained.4.We research the sufficient condition to global exponential stability of almost periodic cellular neural networks with time-varying delays.By nonlinear measure method and the generalized almost periodic Halanay inequality is,we obtain an integral average criterion for global exponential stability of the networks.The examples and their corresponding numerical simulations are presented to illustrate the effectiveness of our methods and correctness of our conclusions.