Stability Analysis of Discrete-Time Recurrent Neural Networks With Stochastic Delay

Abstract—This paper is concerned with the stability analysis of discrete-time recurrent neural networks (RNNs) with time delays as random variables drawn from some probability distribution. By introducing the variation probability of the time delay, a common delayed discrete-time RNN system is transformed into one with sto-chastic parameters. Improved conditions for the mean square sta-bility of these systems are obtained by employing new Lyapunov functions and novel techniques are used to achieve delay depen-dence. The merit of the proposed conditions lies in its reduced con-servatism, which is made possible by considering not only the range of the time delays, but also the variation probability distribution. A numerical example is provided to show the advantages of the pro-posed conditions. Index Terms—Delay dependence, discrete-time recurrent neural networks (RNNs), mean square stability, stochastic time delay. I