Asymptotic mean square stability analysis for cellular neural networks with random delays

摘要

In this paper, the asymptotic mean square stability analysis problem is considered for a class of cellular neural networks (CNNs) with random delay. The evolution of the delay is modeled by a continuous-time homogeneous Markov process with a finite number of states. The main purpose of this paper is to establish easily verifiable conditions under which the random delayed cellular neural network is asymptotic mean-square stability. By employing “delay-averaging” approach we demonstrate how certain stochastic asymptotic mean square stability conditions can be derived in terms of transition functions of the Markov process and stability properties of a system with a constant delay. The criteria based on linear matrix inequalities(LMIs) for the stochastic asymptotic mean square stability is given, which can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A numerical example is exploited to show the usefulness of the derived LMI-based stability conditions.