Robust Stability Analysis For Neural Networks With Neutral Time Delay

Recently, the research and application of neural networks and other problems haveattracted more and more attention. In practical applications, the time delay, the existenceof uncertain parameters and random disturbance often lead to instability of the system andthe system performance. Therefore, the research of neural network stability has importanttheoretical significance and application value.The neural networks with neutral time delay have been studied mainly ranging fromthe neutral time delay，interval parameter uncertainties, random disturbance, and switchingrules. The main contents are as follows:Firstly, for a class of neural networks with neutral time delay, by constructinginnovative Lyapunov function included the triple integral condition, joining the libertyvalue matrix, and combining with the linear matrix inequality (LMI) technique, somesufficient conditions are derived for robust exponential stability of the equilibrium point ofthe system. The results obtained in this paper are little conservative compared with theprevious results in the literature. Two examples show the validity and feasibility for theproposed criteria.Secondly, the robust stability problem of a class of interval stochastic neuralnetworks with neutral time delay is discussed. Using proper Lyapunov functional method,some inequality analysis techniques, the liberty value matrix, Ito ’s differential equation,utilizing the linear matrix inequality (LMI), some delay-dependent criteria are developed,which guarantee the robust asymptotic stability of the interval stochastic neural networkswith neutral time delay. And the correctness of the theoretical results is validated by anexample.Thirdly, we study the robust stability of interval switching random neural networkswith neutral time delay, relying on switched rule, taking advantage of the method ofstochastic analysis, a novel criterion of robust asymptotic stability is derived, which is inthe form of linear matrix inequality(LMI). Finally, one simulation example is given to illustrate the correctness of the proposed methods.