Robust Stability Analysis For Neural Networks With Non-lipschitz Activation

In the process of implementations of neural networks, uncertainties are inevitable in neural networks by reason of the existence of modelling errors, ex-ternal disturbance and parameter fluctuation. This shows that it is important to study the robust stability of neural networks in the presence of uncertain-ties.In this dissertation, based on the Lyapunov functional method, the topological degree theory, LMI inequality technology, the nerual networks with inverse-Lipschitz neuron activations are investigated.The contents include the global robust exponential stability, the existence and uniqueness of solution and so on.The main works of this dissertation are as follows:The general development and several usual dynamical models of neural networks are reviewed. The importance of studying the dynamical behaviours of neural networks is explained. Also the current status in neural networks are analyzed.The definitions of the stability of neural networks and the needed preliminaries in the stability of neural networks are introduced.The global robust exponential stability of Hopfield neural networks with inverse-Lipschitz neuron activation functions is considered.And a sufficient condition which ensures that the network is globally robustly exponentially stable is established.The global robust exponential stability of interval Hopfield neural networks with delays and inverse-Lipschitz neuron activation functions is considered. By applying Lyapunov functional approach, a sufficient condition which ensures that the network is globally robustly exponentially stable is established.The stability of Cohen-Grossberg neural networks with inverse-Lipschitz neuron activations are analyzed. In Conclusion, the research work of this dissertation is summarized,and the future developing directions are included.