Stability Analysis Of Uncertain Time-varying Delay Neural Network And Robust Control

Neural network system has been widely applied since it was put forward. As vulnerable to the influence of various uncertainty and disturbance, the signal will show delay phenomenon and instability, so to make the research for stability of the time-varying delay system is very meaningful, the problem of stability for uncertain system with time-varying delays is often studied.This paper mainly discusses the exponential passivity for neural networks with multiple time-varying delays, the passivity for neural networks with discrete and distributed delays, the robust asymptotic stability of the fuzzy neural network and the analysis of dissipativity for BAM neural networks. The results are as follows:Part 1. This section will study passive problems for neural network with multiple and mixed time-varying delays(it contains both discrete and distributed delays). By constructing proper Lyapunov functions, then we use inequality technique to deal with the derivatives. According to the need, we introduce some appropriate 0 items to get some linear matrix inequalities, so that we can get the condition to judge the system is passive. Finally examples demonstrate the conclusions obtained are correct and can reduce the conservative to some extent.Part 2. This chapter will study the robust asymptotic stability of the fuzzy neural network with discrete and distributed delays. With the help of T-S model, we change the problems to be linear inequality problems by constructing proper Lyapunov functions, multiple integral, free matrices and inequality techniques. Through Matlab toolbox the examples prove that the conclusion is correct and effective.Part 3. This part we study the global dissipativity of BAM neural networks with discrete and distributed delays. By using Lyapunov stability theory and linear matrix inequality, we construct new functions, then we can get new criteria to judge BAM neural network system with mixed delays is global dissipativity. The last example shows the feasibility of the conclusion.