Stochastic Stability Of Fuzzy Hopfield Neural Networks With Time-Varying Delays

Artificial intelligence with uncertainty is a hot and important research topic now. As a kind of important tool of dealing with uncertain problem, fuzzy neural networks which have merits of artificial neural networks and fuzzy logic systems can simulate the biological structures and some functions of human brains and the characteristics of information processing.The theory and application of the neural networks with time-delay not only has reflected the hardware reality such as limited switch speed of a amplifier in the artificial neural networks, but also better simulates the time-delay character of biology neural networks. Since the stability of the neural networks with time-delay is the foundation of the network's application and the most basic problem, many researchers has been attracted to this field. Most existing results concerning this topic are based on delay-irrespective HNN or constant delay HNN. The actual delays are time-varying in the majority of cases, so, the results are likely to be conservative. So, in this thesis, the following tasks have been accomplished:(1) Some simplification conditions are given on the stability of discrete Hopfield neural networks from mathematics angel while the global convergence condition is discussed. The conclusion of positive definite is modified based on former results, thus, a new conclusion without positive definite can be engendered analogously. Certainly positive definite matrix surely satisfies the 1-positive definite condition, but it is not necessary to satisfy strict mathematic positive definite condition in actual networks.(2) Fuzzy technology are combined with neural networks, and stochastic fuzzy Hopfield neural networks with time-varying delays is investigated through further extending the ordinary T-S models to describe the delayed Hopfield neural networks which are subjected to environmental noise. The global exponential stability in the mean square for this model is studied by using the Lyapunov–Krasovskii approach. Stability criterion is derived in terms of linear matrix inequalities (LMIs), which can be effectively solved by some standard numerical packages. At last the conclusion is illuminated through some numerical examples.