Stability Analysis of Recurrent Neural Networks with Random Delay and Markovian Switching

Abstract

In this paper, the exponential stability analysis problem is considered for a class of recurrent neural networks (RNNs) with random delay and Markovian switching. 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 recurrent neural network with Markovian switching is exponentially stable. The analysis is based on the Lyapunov-Krasovskii functional and stochastic analysis approach, and the conditions are expressed in terms of linear matrix inequalities, 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.