Stability Analysis For Nonlinear Cellular Neural Networks With Delays

Delayed cellular neural networks(DCNNs) have found applicationin many areas such as optimization, siganl processing, image processing,pattern recognition and associative memories, so they have been fullydeveloped. Because the information processing capability of a neuralnetwork is determined by its dynamic behavior, the study of dynamicproperties of neural networks has been one of the most important topicsof research in this area.This thesis addresses the stability of delayed cellular neuralnetworks. First of all, the thesis briefly reviews the fundamentalknowledge, the history and the state-of-the-art of stability of neuralnetworks. On this basis, the thesis makes the following contributions.1) delay-independent stability analysis for cellular neuralnetworks with constant time delayA new stability criteria is derived by utilizing the Lypunove- Krasovskiifunctional method and the matrix inequality approach. The conditionprovide some parameters to appropriately compensate for the tradeoffbetween the matrix definite condition on feedback matrix and delayedfeedback matrix. This criteria is less restrictive and generalizes some ofthe previous stability results derived in the literature. Numericalsimulation result illutrates the effective of the method proposed in thispart. 2) New delay-independent stability analysis for cellular neuralnetworks with constant time delayThis part concerns the global asymptotic stability of celluar neuralnetworks with constant delay. An appropriate type ofLyapunov-Krasovskii functionals and the linear matrix inequatity (LMI)approach and argument matrices are proposed to investigate the problem.An improved global asymptotic stability criterion is also derived that is ageneralization of, and improvement over, previous results. Numericalexample demonstrates the effectiveness of the criterion.3) delay-dependent stability analysis for cellular neural networkswith constant time delayAt first a transformation is made the nonlinear neural networks into thelinear neural networks. Then the Lyapunov-Krasovskii stability theoryfor functional differential equations and the linear matrix inequality(LMI) approach are employed to investigate the problem. A novelsufficient condition is derived that is less conservative than the onesreported so far in the literature. Numerical examples illustrate theeffectiveness of the method and improvement ove some existingmethods.4)delay-dependent stability analysis for cellular neural networkswith time-varying delay A new Lyapunov-Krasovskii functional and the linear matrixinequatity(LMI) approach are proposed to deal with the problem of theglobal asymptotic stability of celluar neural networks with time-varyingdelay. Some parametermatrices are used to express the relationshipsamong the system variables, and among the terms in Leibniz-Newtonformula. As a result, an elegant delay dependent stability for neuralnetworks with time-varying delay is derived that is a generatlization of,and an improvement over, previous criterions. Numerical exampledemonstrates the effectiveness of the condition.5) Stability Analysis for cellular Neural Networks with Random Time DelayThis part deals with the problem of stabilization for a class of cellularneural networks with random time delay. Markov processes are used tomodel random time delay. The random Lyapunov functional and thelinear matrix inequality (LMI) approach are employed to investigate theproblem. A stochastic stability criterion for the system is derived. Someimportant corollaries are derived from the theorem.