Novel stability criteria of generalized neural networks with time-varying delay based on the same augmented LKF and bounding technique

Abstract

This paper researches the stability issue of generalized neural networks (GNN) with time-varying delay. For the delay, its derivative has an upper bound or is unknown. Firstly, the augmented Lyapunov-Krasovskii functional (LKF) is constructed based on the state vectors of the third order integral inequalities. Then, by introducing two sets of state vectors, the LKF derivative is presented as the quadratic and quintic polynomials of the delay, respectively. Next, the new quadratic and quintic polynomial negative definite conditions (NDCs) are proposed to set up the linear matrix inequalities (LMIs). In addition, based on the same LKF and third order integral inequalities, this paper proves that the introduction of extra state vectors increases the conservatism of the derived stability conditions. Eventually, the advantages of the provided conditions are illustrated by several numerical examples.