Stability Of Stochastic Delay Systems And Its Application In Neural Networks

Stochastic delay is widely used in control process, where the current term is also delayed, so the pure delay system more fit the actual. Combining the stability conditions of stochastic delay systems modeled by a finite continuous state Markov chain and the stability conditions of double delay systems, this paper studies the almost sure uniform stability and almost sure uniform asymptotic stability of a double pure delay system. The delay time of the first item is controlled by 1, and the delay time of the second term is the stochastic delay which is modeled by a finite continuous state Markov. The Markov chain involved includes a fast changing part and a slowly varying part. The quasi stationary distribution of the Markov chain is used as the weight measure, then we can get the conclusion that the delay of the average delay of the whole system with almost sure uniform stability and almost sure uniform asymptotic stability of the pure delay system can be obtained by the mean delay of the second delay. This means that, although there are some delays, and the system is not stable, but the whole system is stable. That is to say, the influence of the stochastic delay in the second term is balanced, and this Markov chain exists as a stabilizing factor.In this paper, we obtain the sufficient condition for almost sure uniform stability and almost sure uniform asymptotic stability of double pure delay stochastic systems. The r of this condition shows that the Markov chain acts as a stabilizing factor. In CNNs neural network, Hopfield neural network with time delay is introduced. Meanwhile, applying stability conditions of double pure delay stochastic systems. So we can obtain the sufficient condition for the stability of a kind of CNNs neural networks with special delay.