Global Robust Stability Analysis Of Neural Networks With Multiple Time Delays

Stability analysis is not only a basic issue of neural networks, but also an important issue in dynamic systems theory. In electronic implementation of neural networks, there exist inevitably time delays and some uncertainties due to the existence of delayed transmission of signals, modeling errors, and external disturbance, which may influence the stability of the entire network by creating oscillatory or unstable phenomena. So it is very important to study the stability of the uncertain systems. In this thesis, the robust stability of neural networks with multiple time delays is studied.The first chapter outlines the introduction on the most basic questions that are related to artificial neural network, stability of dynamic system and the Lyapunov stability theory.The second chapter derives some new criteria on the global robust asymptotic stability of the following neural network modelBy using a homeomorphism mapping that is associated with the model, the existence and uniqueness of equilibrium point of this model is proved. By combining suitable Lyapunov functional with the matrix inequality technique, the global robust stability of the equilibrium point is deduced.The third chapter gives the some new sufficient conditions on the global robust asymptotic stability of the following modelSince the model can not be similarly transformed into a simple vector-matrix form as that in second chapter, some improved approaches are employed to obtain the desired results.Theoretical analysis and examples are given in the second and third chapter to illustrate that the results in this paper have a broader scope of application than some existing results in the literature.