The Stability And Stabilizability Of Stochastic Neural Networks

In recent years, the dynamical issues of stochastic delayed neural network shave attracted worldwide attention. Many interesting stability criteria for theequilibrium solutions of stochastic delayed neural networks have been obtained. Inthis thesis, I investigate the stochastic, the pth moment exponential stability andthe almost sure exponential stability of the equilibrium solutions. Two specialtypes of stochastic neural networks are studied in this paper, they are stochasticHopfield neural networks and Cohen-Grossberg neural network s. I study thesufficient conditions of the guaranteeing the stability and stabilization forstochastic Hopfield neural networks and stochastic Cohen-Grossberg neuralnetworks.Firstly, as the introduction, the background and development of the study o fthe stability and stabilization for stochastic neural networks are presented. Theinnovation points and outline of this work are also given in this paper.Secondly, I mainly describe the sufficient conditions that can gu arantee thestability for stochastic interval Hopfield neural networks with variable delay andstochastic Hopfield neural networks with mixed delay. The robust stabilizationabout the stability for stochastic Hopfield neural networks is also studied. Bychoosing the reasonable Lyapunov-Krasovskii function, employing some inequalitytechnique, we can get the sufficient conditions with the delay–dependent robuststabilization by the form of LMI.Lastly, two things are introduced, which are the stability for stochastic Cohen-Grossberg neural networks with LMI and the stabilization for stochastic Cohen-Grossberg neural networks with the distribution parameters. When stabilization ofstochastic Cohen-Grossberg neural networks with the distribution parameters isconsidered, a state feeback controller is designed, in which the gain matrix can begot by solving a linear matrix inequality and therefore it can be easily utilized inpractical engineering.