Stochastic Delay Neural Network With Pulse Synchronization Analysis

This thesis focuses on the global mean-square synchronization for a class of impulsive stochastic neural networks with Markovian parameters. The neural networks under consideration involve both discrete time-delay and distributed time-delay. The impulsive control with merits such as simple realization, low control cost and small energy consumption is attracting the interests from the control community. The impulsive control is extensively used in chemical industry, electronic techniques and traffic systems, and is also successfully used in chaotic control and in chaotic privacy communication. Now The impulsive control has become one of hot topics in engineering and control. In this thesis, by constructing novel Lyapunov-Krasovskii functionals and using some new analysis technique, the sufficient conditions are derived to guarantee the mean-square synchronization for the neural networks studied. The above analysis is further generalized to deal with the uncertain neural networks and obtain the robust synchronization criteria. All the criteria can be expressed in form of LMI and can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. It is worth mentioning that the criteria are derived without assuming that the activation functions are bounded, monotone and differentiable. Finally, the numerical examples are given to demonstrate the proposed methods.This thesis consists of three parts. The first section begins with a brief introduction to the related background and significance for the research on delayed networks and impulsive systems. And then we introduce the latest progress in investigation for delayed neural networks with Markov chain.In Section 2, we formulate the problems to be dealt with in this thesis.In Section 3, we first introduce the neural network models to be investigated. By constructing new Lyapunov-Krasovskii functionals, we obtain the sufficient conditions for the neural networks studied to be synchronous in the mean square, and further extend the related results to the uncertain neural networks. We conclude this thesis with a numerical example to show the effectiveness of the proposed methods.