The Stability Analysis For Several Types Of Delayed Cellular Neural Network Models

This paper focuses on the global asymptotic stability and exponential stability of several types of cellular neural networks with time-varying delays. These mod-els have found many applications in a variety of areas, such as signal processing, pattern recognition, static image processing, associative memory, combinatorial optimization,and other areas. By studying these models, we can understand the structure of certain features of its own. Various applications of neural networks depend on the stability characteristics of neural networks, therefore, the stability of neural networks has important theoretical and practical significance. This paper is composed of three chapters.In Chapter 1, history of the development of neural networks are briefly re-viewed, and the current situations in the field are summarized. This paper proposed a number of issues to be discussed and the significance of the results.In Chapter 2, we mainly discuss global asymptotic stability of neural net-works with time-varying delays. Firstly, we discuss the asymptotic stability of a time delay neural network model, the research on this model has achieved very abundant achievements. By constructing new Lyapunov function and using lin-ear matrix inequality method, some new sufficient conditions of the existence and global asymptotic stability are obtained. Secondly, bi-directional associative mem-ory network system for the global asymptotic stability are investigated via a similar approach.In Chapter 3, we investigate the time-delay neural network system for global exponential stability. In section 1, we describe the multiple-time-delay neural net-work system for global exponential stability. By using the Halany inequality, and constructing a Lyapunov function, we discuss its stability. In section 2, we discuss the variable coefficients and time-varying delay neural network model, using linear matrix inequalities and the corresponding Lyapunov function, we obtain some new results.In order to illustrate the effectiveness of the method, in the back of each section, using the LMI toolbox in Matlab software, we verify the validity of the proposed method by some examples.