| Neural network is a highly synthetic interdiscipline. It is a kind of intelligent control technology. In recent years, the neural network becomes one of "hot spots" in scientific research. Stability can make the normal operation of the system and robustness can make an effect in abnormal and dangerous situations in the system. Therefore, the stability and robustness are very important when we study the neural network.The stability analysis of three uncertain neural networks with time-varying delays is investigated in this thesis based on Lyapunov stability theory and linear matrix inequality (LMI) technology. Sufficient conditions are given to ensure the stability of neural networks. Compared with some existing results, the criteria obtained in our paper are less conservative.Firstly, a novel Lyapunov function is constructed to investigate the robust exponential stability in mean square for uncertain stochastic neural networks. A new criterion is derived in terms of linear matrix inequalities. A numerical example is given by LMI control toolbox in Matlab to demonstrate the effectiveness of our results.Secondly, a class of Markovian jumping impulsive stochastic Cohen- Grossberg neural networks with discrete and distributed time-varying delays is considered. Applying the inequality technique and stability theory, several new sufficient conditions are obtained to ensure global robust asymptotic stability in the mean square. The stability theorem has a better application. In the end, an example is provided to illustrate the effective of our theorem.Thirdly, a class of discrete stochastic neural networks with discrete and distributed time-varying delays is studied. By constructing a new Lyapunov functional, the theorems are achieved to ensure the asymptotic stability. The theorems are obtained in the form of linear matrix inequality which can be calculated by LMI Toolbox in Matlab. An example is provided to show the effectiveness and applicability of our theorem. |
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