An LMI approach to stability analysis of stochastic high-order Markovian jumping neural networks with mixed time delays

Abstract

This paper deals with the problem of global exponential stability for a general class of stochastic high-order neural networks with mixed time delays and Markovian jumping parameters. The mixed time delays under consideration comprise both discrete time-varying delays and distributed time-delays. The main purpose of this paper is to establish easily verifiable conditions under which the delayed high-order stochastic jumping neural network is exponentially stable in the mean square in the presence of both mixed time delays and Markovian switching. By employing a new Lyapunov–Krasovskii functional and conducting stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the criteria ensuring exponential stability. Furthermore, the criteria are dependent on both the discrete time-delay and distributed time-delay, and hence less conservative. The proposed criteria can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A simple example is provided to demonstrate the effectiveness and applicability of the proposed testing criteria.