Study On The Stability Of Neural Networks With Time - Varying Delay

The delay-dependent global asymptotical stability of three classes of delayed neural networks have been studied by using Lyapunov functional method and newly delay interval decomposing approach. We derived some improved delay-dependent stability criteria. The obtained results are less conservative than some existing results.The main works of this thesis are as follows:We derived some global asymptotic stability conditions for neural networks with time-varying delay. By decomposing the delay interval into multiple subintervals and constructing a new Lyapunov functional, we derived some new delay-dependent stability criteria. The obtained criteria are less conservative because the Jensen inequality, free-weighting matrices method and inverse convex approach are used. Finally, we use an numerical example to indicate the merits of the derived results.We derived some global asymptotical stability conditions for neural networks with distributed time-varying delay. By decomposing the delay interval into multiple subintervals and constructing a new Lyapunov functional, we derived some new delay-dependent stability criteria. The obtained criteria are less conservative because the Jensen inequality and the improved inverse convex approach are used. Finally, we use an numerical example to indicate the merits of the derived results.We studied the problem of global asymptotic stability criteria for neural networks with interval time-varying delay. Based on the the newly delay interval decomposing approach, an improved Lyapunov functional is constructed. The obtained criteria are less conservative because the inverse convex approach and activation function interval decomposing approach are used. Finally, we use an numerical example to indicate the merits of the derived results.