Analysis For Several Classes Of Neural Networks Stability With Time Delay

In this dissertation, based on the Lyapunov functional method, matrix theory and the topological degree theory, LMI inequality technology and analysis skill, the continuing and discreting dynamical behaviours of several classes of neural networks, which are described by the differential equations whose vector space is the functional differential equations, are investigated. The contents include the global exponential stability,global asymptotically stability,the existence and uniqueness of solution and so on.The main works of this dissertation are as follows:The general development and several usual dynamical models of neural networks are reviewed. The importance of studying the dynamical behaviours of neural networks is explained. Also the current status in neural networks are analyzed, and neural networks for solving optimal problem are briefly introduced.We choose a Lyapunov function to suit neural networks, through researching in theory of stability and neural networks, and then dispose the matrix with some skills. We get a better liner matrix inequality result, including global asymptotically stability, global asymptotically robust stability and exponential stability. In this thesis we present delay-dependent stability criterion, so as to get the maximum numerical delay and some results independent of the delay parameters easily. At last, we present numerical examples to illustrate the effectiveness of the results and turn out to be a generalization and improvement over some previous stable criteria.A new class of neuron activation functions which are called inverse Lipschitz functions (ILF) is introduced , and some properties of ILF are produce. First, a novel class of delayed neural networks with inverse Lipschitz functions, which is investigated, is developed. the local existence of solutions for the neural network is proved. By constructing appropriate Lyapunov functions , the global existence of solutions is given. The existence of the equilibrium point of the neural networks is proved by topological degree theory. Finally, by using linear matrix inequality and constructing appropriate Lyapunov functions, global exponential stability of the neural network are investigated, some sufficient conditions which are used to ensure the exponential stability are given.Applying invers Lipschitz condition to the C-G neural networks modal. The existence of the equilibrium point of the neural networks is proved by topological degree theory. Finally, by using linear matrix inequality and constructing appropriate Lyapunov functions, global exponential stability of the neural network are investigated, some sufficient conditions which are used to ensure the global exponential stability are given.Global exponential stability of a class of neural networks with distributed delays is investigated by matrix measure technique and Halanay inequality. Several sufficient condition are given to guarantee global exponential stability of the neural networks without assumption differ entialiability of delay ,the bound and the monotonicity of neuron activations. At last ,example are given to illustrate the application of our resultes.We give a research on the stability of The Discrete Hopfield neural network(DHNN) . Some simplification conditions are given on the stability of DHNN . Also the global convergence condition is discussed. the stability of DHNND is investigated, mainly including the stability of parallel, serial and general updating rule. For the fist time, the condition that the matrix need is weakened by the decomposition to the time delay matrix and introducing the parameter; When the threshold value is zero, the stability of DHNND is studied with the initial state X (0)≠X(1). The updating property of DHNND with general updating rule is given, which provides a certain theory to the optimized problem.Given the design method of the discrete Hopfield neural network with associative memory ,Which producted by means of memorizing value condition in local domain. The solution of inequality set is the coefficient (Q,c) of discrete quadratic energy function So weight matrix and threshold value vector may be decided directly.In Conclusion, the research work of this dissertation is summarized,and the future developing directions are included.