Global Stability And Dissipativity Analysis Of Neural Networks With Time Delays

The paper firstly introduce the development process of neural networks, the background and importance of the research subject, and the current research status of delayed neural networks and dissipativity systems. The main contents of this dissertation discuss the global asymptotic stability and the global robust stability of neural networks with time-varying delays, as well as global robust dissipativity of neural networks with variable and unbounded delays. In this paper, we derive a series of sufficient conditions for stability and dissipativity by using Schur complements, Lyapunov functionals and other techniques. The obtained criteria improve and develop the previous results in some literatures.The main works are listed as follows:1. We study the global asymptotic stability of cellular networks with time-varying delays by using Lyapunov functional and Schur complements. The sufficient criteria obtained here can be solved by software packages in MATLAB .2. Based on the proper Lyapunov functionals, linear matrix inequality and other inequality techniques,some sufficient conditions are presented for global robust stability of neural networks with time-varying delays. And it is shown that the new results which are independent on delay impose weaker conditions for the robust stability. An example with its simulation is provided to demonstrate the usefulness of the proposed criteria.3. This paper presents some new less conservative conditions for the global robust dissipativity of neural networks with variable and unbounded delays by using Lyapunov functionals and inequality techniques. Comparing with earilier literatures,the results of this paper are effective.