Stability Analysis For Several Classes Of Neural Network With Time Delays

Delayed recurrent neural networks exhibiting high intelligence are a class of nonlinear dynamical system. Since delayed recurrent neural networks have had a wide application on signal processing, artificial intelligence and other fields, the study of the stability of recurrent neural networks is of great value. In this dissertation,we focus on the stability problem of Hopfield Neural Networks with distributed delays, the uncertain Hopfield Neural Networks with neutral delay and the exponential stability problem of Cohen-Grossberg Neural Networks(CGNN) with infinite distributed delays and impulses. The main contents of this dissertation are as follows:By using Lyapunov-Krasovskii functional theory, a reasonable LyapunovKrasovskii function is defined. Based on lemma 1.4.4, theorem 1.4.4 and the condition of the generalized Lipschiz, a sufficient criterion ensuring the exponential stability of Hopfield Neural Networks with distributed delays is obtained. Suitable examples which support the theory are also presented by LMI toolbox in MATLAB.Based on Lyapunov-Krasovskii functional theory, lemma 1.4.1 and leaded in the real matrix 2P,3P with appropriate dimension, the sufficient condition are derived to ensure the asymptotic stability of the uncertain Hopfield Neural Networks with neutral delay. Suitable numerical examples which support the theory are also given.By applying Lyapunov-Krasovskii functional theory and linear matrix inequality(LMI) technique, utilizing the lemma 1.4.2, theorem 1.4.4, the sufficient condition under the assumptions(I) ―(VII) ensuring the exponential stability for CohenGrossberg neural networks with infinite distributed delays and impulses is obtained. The numerical example is provided to illustrate the effectiveness of the theoretical results.