The Stability Of Neutral Delay Neural Network Analysis

This paper is concerned with the stability for neutral-type neural networks. In recent years, neural networks with delays have important applications in many fields, such as associative memory, Image processing and optimization calculation. With the development of electronic technology, people have found that we consider not only the influence of past state on now, but also the change of past state on now, which is neutral delay. As is well-known, time delays often cause systems instability or performance deterioration. The study of stability for this system has important theoretical significance and application value. In this dissertation, we study the asymptotic stability and exponential stability for the neutral-type delayed system by constructing Lyapunov-Krasovskii functional and estimating its derivative with integral inequality, and some sufficient conditions are derived to assure that the system is stable.In our thesis contents are organized as follows:The first chapter introduces the research position of neural networks at home and abroad, and illustrates its theoretical significance and application value. At last we show the main work of this article.The second chapter describes the basic theory involved in paper, including basic concepts about neural networks and its stability, main lemma and important inequality for studying the stability.The third chapter analyzes the global asymptotic stability for the neutral neural networks with a constant delay. Firstly we construct a new Lyapunov-Krasovskii functional, by dividing the constant delay into equal flat segments. Then we get a few asymptotic stability criterions, combining Lyapunov-Krasovskii stability theorem with linear matrix inequalities. This criterion can be verified by MatlabLMI Toolbox. Simulation results show that the results of this paper have less conservative compared with the existing literatures.Chapter Four analyzes the global asymptotic stability for the neutral-type system with a time-varying delay. In this chapter, the discrete time delay and neutral are time-varying function. Using Lyapunov-Krasovskii functional method, we get asymptotic stability condition for this system with a new Lyapunov-Krasovskii functional, which is constructed by splitting the upper bound of the time-varying delay. As examples show, this condition is less conservative.ChapterⅤdiscusses the global exponential stability for neural network with distributed delay. Thinking of the method of constructing Lyapunov-Krasovskii functional in the first two chapters, we obtain the exponential stability results for this neural network. Here the integral cross-term treatment is made by introducing a less conservative inequality results.