Stability Analysis Of Neural Networks With Time-Varying Delays

Neural networks is a kind of intelligent control technology, which can simulate human being's intelligent behavior, solve many complicated and nondeterministic nonlinear automation problems not settled by traditional automaton technology. Therefore, during the last several decades, the study of neural networks has aroused the general interest of academic field. The theory and application of the neural netwotks with time-delay is one of the international foreland problems at present. The time-delay not only has reflected the hardware reality such as limited switch speed of amplifier in the artificial neural networks, but also better simulates the time-delay character of biology neural networks. At the same time, it is the need to solve certain actual problem.Based on Lyapunov stability theory and linear matrix equality (LMI) technology, the stability analysis of several neural networks with time-varying delays is investigated in this thesis. Sufficient conditions are given in terms of LMIs to ensure the stability of neural networks. Compared with some existing results, the criteria obtained in our paper are less conservative.Firstly, the robust stability problem for a class of uncertain cellular neural networks with norm-bounded uncertainties is considered in this paper. The conditions are proposed to guarantee the asymptotic and exponential stability of neural networks, which are dependent on the time-varying delays. And we don't need the restriction that the derivative of time-varying delay is less than one. A numerical example is given to illustrate the effectiveness and improvement over some existing results.Secondly, the global exponential stability is investigated for a class of stochastic neural networks with time-varying delays and norm-bounded uncertainties or interval uncertainties. Based on Lyapunov stability theory and stochastic analysis approaches, the delay-dependent criteria are derived to ensure the global, robust, exponential stability of the addressed system in the mean square for all admissible parameter uncertainties. A numerical example is given to illustrate the effectiveness and improvement over some existing results.Thirdly, the global asymptotic stability is investigated for a class of neutral stochastic neural networks with time-varying delays and norm-bounded uncertainties. Based on Lyapunov stable theory and stochastic analysis approaches, the delay-dependent criteria are derived to ensure the global, robust, asymptotic stability of the addressed system in the mean square for all admissible parameter uncertainties. A numerical example is given to illustrate the effectiveness of our results.In the end, the problem of robust asymptotic stability analysis of stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays is studyed. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technology, some sufficient conditions are derived to ensure the global robust convergence of the equilibrium point. A numerical example is given to demonstrate the effectiveness and improvement of our results.