Stability Analysis Of Neural Networks With Multiple Time-varying Delays And Uncertainties

As one kind of Artificial intelligence, neural network has got a lot of achievements in the theoretical study and practical applications. Since 1982, Hopfield neural network, related stability concept and energy function are proposed, which gradually arouses many scholars’interest. Delay phenomenon exists widely in various industrial processes, which is one of the important reasons leading to system instability or performance degradation, meantime it becomes a hot topic of the control area and control engineering. Compared to the dynamic systems with fixed time delay, the neural network model with time-varying delay is better to simulation of control system. General dynamics will be accompanied by some uncertain disturbance, therefore, in the system simulation time, coupled with appropriate uncertainty factors in the reality problems must be considered. So the study of neural networks with time-varying delays and robust stability has important significance. In this paper, the neural networks with time-varying delays and uncertain factors are discussed by the application of Lyapunov-Krasovskii functional method, linear matrix inequality and free weighting matrix. This paper gives the stability criterions and a numerical example to illustrate the validity of the conclusions. The main contents of this paper are as follows:Chapter1. Introduction. The first chapter gives the history of neural networks and its current research status.Chapter2. Preliminary knowledge. This chapter describes some used preliminary knowledge and some symbol description.Chapter3. The stability analysis of neural networks with multiple time-varying delays.This chapter discusses the neural networks with time-varying delay stability problem. In the course of the discussion, neural network system with two time-varying delays are fist discussed and new stability criterions are proposed with the help of Lyapunov-Krasovskii functional method. A numerical example is given to illustrate the validity of the conclusions. And then the question is extended to contain multiple time-varying delay system, and new stability criterions are put forward.Chapter 4. The stability analysis of neural networks with multiple time-varying delays and uncertain factors. The fourth chapter discusses neural networks with time-varying delays and uncertain factors. The uncertain factors are norm-bounded uncertainty. In discussing the stability criterion, two time-varying delays uncertainty neural network are discussed and then extend it to multiple time-varying delays.Chapter 5. Summary and Prospect. This chapter gives a summary to this article and gives research prospect of neural networks.especially neural networks with time-varying delays based on current research status.