The Stability Of Neural Network With Variable Time-delay

Recent years stability criteria of neural networks have been studied more extensively and have been widely applied within some kinds of engineering fields such as associative memories, combinatorial optimization, population dynamics,pattern recognition,image processing, and computing technology and so on.It is well known that time delays naturally occur in the practical systems and frequently results in instability and oscillations or other poor performances in the many different areas and neural networks systems.Therefore, the problem of stability analysis of neural networks with time-delay is more and more important in both theory and practice.In this paper,I mainly discuss stabilities of three types neural networks. Firstly, we discuss the improved and new robust passivity stability criteria of neural networks with discrete and distributed time-varying delays.We usually use Jensen’s inequality to handle integral inequalities or free matrix approach.We will see many ways which is more accurate than Jensen’s inequality to deal with the derivative of Lyapunov fuctional or the integral item which was divided into several subintervals,then,we handle every subintervals by different ways to reduce the conservatism of neural networks.Secondly,we discuss the criteria of cellular neural network with continuous time-varying delay including the neural networks systems with a single time delay.We can obtain our results by constrcting Lyapunov functional, dealing with the derivative,discussing the relation between upper and lower bound separated more subset,using different inequality,adding zero item to reduce the conservatism of neural networks.Finally,we discuss the criteria of neural network of robust stability with a single neutral time-varying delay.Neutral delay neural network system is a kind of more special time-delay systems.It is neural network system which related not only the state of the past but also now.So it is more difficult and complex than others situation to study. We can use Lyapunov stability theory to reduce the conservatism of neural networks by using appropriate Lyapunov functional and different inequality and adding zero item to obtain our results.