Global exponential stability analysis of neural networks with a time-varying delay via some state-dependent zero equations

Abstract

This paper studies the exponential stability problem of neural networks with a time-varying delay. Firstly, an augmented Lyapunov-Krasovskii functional (LKF) containing a single integral state is constructed. Then a generalized free-matrix-based integral inequality and the auxiliary function-based integral inequality combined with an extended reciprocally convex matrix inequality are used to estimate the derivative of the LKF. The novelty of this paper is that some state-dependent zero equations are introduced into before and after bounding the LKF’s derivative so as to increase the freedom and reduce the conservatism. As a result, a less conservative stability criterion is derived in the form of linear matrix inequality, whose superiority is illustrated with three numerical examples.