Stability Analysis Of A Class Of Cohen-Grossberg Neural Networks With Time-Varying Delays

Since Hopfield proposed a class of fixed-weight recurrent neural networks, and introduced the energy function to study its stability, this kind of neural network was widely applied in parallel computation, combinatorial optimization, pattern recognition, and associative memories, etc. Since Cohen-Grossberg neural networks can denote many kinds of network models and has obvious advantages, the studies on the dynamical characteristics of the model have been paid much attention. The stability analysis for a class of delayed Cohen-Grossberg neural networks is carried out in this dissertation. Based on Lyapunov stability theory and linear matrix inequality technique, the stability problem for Cohen-Grossberg neural networks and fuzzy Cohen-Grossberg neural networks with discrete delay is studied, especially for stability of Cohen-Grossberg neural networks with non-negative amplification function by using nonlinear complementary theory. The main innovations of the dissertation can be briefly described as follows:1. The stability of Cohen-Gorssberg neural networks with discrete time-varying delay is studied. According to definition of homeomorphism map, the uniqueness of equilibrium for Cohen-Grossberg neural networks with different-type delays. Then, by choosing Lyapunov functional and linear matrix inequality technique, the delay-dependent global asymptotical stability of the network can be obtained, where the delay is bounded and its time derivative is smaller than 1.2. The stability of fuzzy Cohen-Grossberg neural networks with time-varying delay is studied. The time-varying delay is assumed to be bounded and its time derivative is smaller than some positive constant. Applying Lyapunov stability theory, two delay-independent exponential stability criteria are proposed based on the expression of linear matrix inequality. The numerical examples can verify the effectiveness of the proposed results. Meanwhile, compared with the results of previous literature, our results have wider range of application.3. The stability of delayed Cohen-Grossberg neural networks with non-negative amplification function is studied. Firstly, the stability of Cohen-Grossberg neural networks with single delay is given. Then, the corresponding result for the case of multiple delays can be obtained. According to nonlinear complementary problem, Lyapunov stability theory, and linear matrix inequality technique, the sufficient condition on the uniqueness and global stability of equilibrium of the networks is proposed. Meanwhile, since the delayed Cohen-Grossberg neural network with non-negative amplification function is more general model, it means that our results have wider range of application.4. The robust stability of Cohen-Grossberg neural networks with parameter uncertainties and non-negative amplification function is studied. By constructing the Lyapunov functional, using the definition of homeomorphism map and linear matrix inequality, the global robust stability criterion can be obtained for the bounded parameter uncertainties. Since the less assumptions are requested, the proposed results is more suitable in practical.