Lagrange stability and passivity in the mean square sense of discrete-time stochastic Markovian switched neural networks with time-varying mixed delays

Abstract

In this paper, the Lagrange stability and passivity of a class of discrete-time stochastic Markovian switching neural networks with mixed delays are studied. The mixed delays include time-varying transmission and distribution delays. Global exponential Lagrange stability criterion and passivity criterion in the mean square sense are derived. A numerical example illustrates the usefulness of these criteria. The originality of the proposed method lies in: (i) the criteria are derived directly from the definitions rather than constructing Lyapunov–Krasovskii functional; (ii) the inequalities in the criteria contain only a few decision variables, which is easy to solve and leads to low computational complexity.