Stability Analysis For Some Classes Of Time Delays Neural Networks Systems

In 1982, Hopfield proposed the Hopfield neural networks, the relevant energy functions and stability concept. This is a milepost of the rapid development for the neural networks. So far, after researchers'assiduous and unremitting efforts, the neural networks have made rapid development both in theory and in practice, and let people have come to realize the importance and considerable foreground of application for neural networks. Delay phenomenon often exists in the neural network systems, and often causes instability and shocks of neural network systems. At the same time, there are many types of time delays, and different time delays show different dynamic characteristics. So it is significantly important in theory and practice to qualitatively study the stability of many types of delays neural networks.Two classes of neural networks with neutral-type delays are focused on in this article. One is the asymptotical stability analysis for neural networks with neutral-type time-varying delays; Another is the robust stability analysis for uncertain neural networks with time-varying delays and neutral-type time delays. The method of Lyapunov-Krasovskii stability theory is used in this article, and some mathematic assumptions and lemmas are proposed to linearize the studied systems. The less conservative stability criteria are obtained by linear matrix inequality. The main works of this paper are as follows:In the first chapter, introduction, the background on stability and application of time delays neural networks systems is introduced. At the same time, the basic theory of knowledges and symbols illustration are given in this chapter.In the second chapter, the neutral-type time-varying delays are added to the mathimatical model of the studied neural networks, and the necessary of mathematical assumptions and lemmas are proposed, then a asymptotical stability criterion in the form of linear matrix inequality is obtained by constructing a suitable Lyapunov-Krasovskii function. Besides, two numerical examples are given to illustrate the effectiveness of the proposed criterion, and the LMI toolbox of Matlab is applied to verify the criterion and obtain the dynamic behaivior of the state in numerical examples.In the third chapter, the time-varying delays and neutral-type delays are added to the mathimatical model of the studied uncertain neural networks. At the same time, some mathematical assumptions and lemmas are given and a suitable Lyapunov-Krasovskii function is constructed. Both a asymptotical stability criterion and a robust stability criterion in the form of linear matrix are gained by linear matrix inequality theory. At the same time, three numerical examples are given to illustrate the effectiveness of the proposed technique with the analysis of results and the simulation figures of systems.In the fourth chapter, conclusions and prospects, concrete conclutions of this paper are given, and further study prospects for delay neural networks are also given by the current research status.