Allowable delay set flexible fragmentation approach to passivity analysis of neural networks

This paper addresses the passivity issue of neural networks with a time-varying delay. We introduce an allowable delay set flexible fragmentation approach for constructing a novel Lyapunov-Krasovskii functional (LKF). Unlike some existing methods, this LKF is more flexible as it allows for different Lyapunov matrices in different allowable delay subsets. Based on the proposed LKF, and utilizing integral inequality approaches and zero equation techniques, several passivity criteria are derived for neural networks with a time-varying delay. Two numerical examples are finally provided to demonstrate the advantages of the proposed method.