New result for generalized neural networks with additive time-varying delays using free-matrix-based integral inequality method

Abstract

This paper investigates the problem of stability for generalized neural networks (GNNs) with additive time-varying delays. Different from previous literatures, a new augmented Lyapunov–Krasovskii functional (LKF) has been constructed. In this LKF, two augmented terms are constructed to establish the interaction among the state vectors with additive time delay upper bounds. In addition, in consideration of the information for two upper bounds, a single and a double integral terms which contain the two upper bounds of additive time-varying delays are firstly introduced to analyze the GNNs. So, based on those treatments, the information about upper bound of additive time-varying delays is sufficiently used. On the other hand, the free-matrix-based integral inequality which can deal with the time-varying delays directly is employed to bound the derivative of the LKF. Based on above works, less conservative criterion is finally derived. Numerical example is provided to show the effectiveness and less conservatism of the proposed results.