Asymptotic Stability And Global Exponential Stability Of Neural Networks With Multiple Time-varying Delays

Time delay is commonly encountered in the implementation of neural networks due to the finite speed of information processing,and it is frequently a source of oscillation and instability in neural networks.The stability analysis of delayed neural networks has received considerable attention and remarkable results have been obtained.In this thesis,we discuss the stability of a more general class of neural networks with multiple time-varying delays.In this thesis,the nonlinear activation functions of neurons are only required to satisfy the Lipschitz conditions.By using the linear matrix inequality(LMI) and Lyapunov functional,we derive some new sufficient conditions for the global asymptotic stability and global exponential stability of the equilibrium point of such neural networks with multiple time-varying delays. These conditions can be easily verified which improve and extend the previous results.Finally, some numerical examples are presented to illustrate that our results are less conservative than existing results derived in the Literature.This thesis consists of three chapters.The 1st chapter simply introduces the research and the main results on the stability of the different classes of neural networks in recent years.The 2nd chapter introduces the concept of global asymptotic stability,and gives the conditions of globally asymptotic stability by the Lyapunov direct method,combined with Brouwer fixed point theorem and an equivalent of the Lyapunov equation.The main results are transformed as the linear matrix inequalities(LMIs) which can be solved efficiently.Meanwhile,some numerical examples are given to show the difference of our results.The 3rd chapter introduces the concept of globally exponential stability,and presents new sufficient conditions of globally exponential stability of neural networks with multiple time-varying delays by using a positive symmetric matrix and constructing suitable Lyapunov functional.Finally,an example is given to compare our results with previous ones.