Stability Analysis Of Two Kinds Of Neural Networks With Multiple Time Varying Delays

Neural networks have been successfully applied to many kinds of fields such as imageprocessing, pattern recognition, parallel computing, associative memories, optimization,partial differential equations solving and so on since they were proposed, and theirapplications have achieved notable development. The stability analysis is one of key issues inneural networks, and has been extensively investigated. Global exponential stability analysisof two kinds of continuous neural networks with multiple time varying delays are studied, andsome sufficient conditions of stability are obtained. This paper is divided into four chapters.Chapter 1 is introduction, and it mainly involves the proposition of neural networks and thesignificance of stability analysis, the models of neural networks studied in this paper,thestability theory in dynamics and the main work in this paper.In chapter 2, based on linear matrix inequality technique, a kind of cellular neuralnetworks with multiple time varying delays is studied. Two delay dependent globalexponential stability conditions are presented in this chapter by defining a newLyapunov–Krasovskii functional. Two illustrative examples are given to demonstratethe effectiveness of the proposed results in numerical examples by matlab toolbox. Theestimations of maximum bounds of time delay and exponential convergence rate bystability conditions in this paper are less conservative than the existing results.In chapter 3, a kind of BAM neural networks with time varying delays is studied, anda delay dependent global exponential stability condition is presented in this chapterby defining a new Lyapunov–Krasovskii functional .It is applied to cellular neuralnetworks with single time varying delay, and a delay dependent global exponentialstability condition of cellular neural networks with single time varying delay is obtained.The effectiveness of the proposed results in this chapter is demonstrated in numericalexamples by matlab toolbox. The estimations of maximum bounds of time delay andexponential convergence rate by stability conditions in this paper are also lessconservative than the existing results.At last, results in this paper are summarized. Stability analysis of neural networks is alsoforecasted and the aim of further research is pointed out.