Delay-Dependent Criteria for Global Robust Periodicity of Uncertain Switched Recurrent Neural Networks With Time-Varying Delay

In this paper, we introduce some ideas of switched systems into the field of neural networks and a large class of switched recurrent neural networks (SRNNs) with time-varying structured uncertainties and time-varying delay is investigated. Some delay-dependent robust periodicity criteria guaranteeing the existence, uniqueness, and global asymptotic stability of periodic solution for all admissible parametric uncertainties are devised by taking the relationship between the terms in the Leibniz-Newton formula into account. Because free weighting matrices are used to express this relationship and the appropriate ones are selected by means of linear matrix inequalities (LMIs), the criteria are less conservative than existing ones reported in the literature for delayed neural networks with parameter uncertainties. Some examples are given to show that the proposed criteria are effective and are an improvement over previous ones.

I. Introduction

Recently, delayed Hopfield neural networks (HNNs) and delayed cellular neural networks (CNNs) have attracted considerable attentions. The dynamics of HNNs with delays have been deeply investigated due to its applicability in solving associative memories, optimization solvers, and signal processing problems, and the dynamics of delayed CNNs have been also deeply studied due to its applicability in solving some image processing, signal processing, and pattern recognition problems; see [1]–[12] for some recent results.