Research On Stability And State Estimation For Complex-valued Neural Networks With Time Delays

In recent years, the complex-valued neural networks(CVNNs for short) have received more and more attention, due to extensive applications in many engineering areas, such as information, electrical engineering, and control engineering. The above-mentioned applications depend largely on the dynamic behavior of the CVNNs. Consequently, the dynamical issues of delayed complex-valued neural networks have been received considerable attention. Recently, many interesting results such as global stability(including asymptotic stability, robust stability, and exponential stability, etc.) criteria for the equilibriums or periodic solutions, bifurcation and chaos of delayed complex-valued neural networks have been derived.This thesis focuses on stability and state estimation of complex-valued neural network with time delays. The main contributions and originality contained in this dissertation are as follows:(1)The global stability of BAM complex-valued neural networks with time delays is investigated. Based on the Lyapunov function method and mathematical analysis technique, sufficient conditions for the global asymptotic stability of the equilibrium are derived by separating complex-valued neural networks into real and imaginary parts.(2)On the basis of complex-valued neural network stability, the state estimation problem of complex-valued neural network is discussed. For the state estimation problem of complex-valued neural network, the purpose is to use the measurable output to estimate the state of the neuron, it concludes that its error system is globally stable. By using Lyapunov stability theory and inequality technique, in the presence of linear matrix inequalities is given in the form of a state estimator. For the complex-valued neural network, many real-valued neural networks dealing skills and qualifications are not suitable. We obtain the gains matrix of the estimator which requires us must establish an error system with new conditions and presents the conditions of asymptotic stability. Finally we prove the effectiveness of method through the data instances and images.