Novel stability analysis methods for generalized neural networks with interval time-varying delay

Abstract

This paper deals with the stability analysis of generalized neural networks (GNN) with interval time-varying delay, and some novel stability criteria are proposed. For the delay, more specifically, it has the upper and lower bounds but the information of its derivative is unknown (or itself is not differentiable). Firstly, a new Lyapunov-Krasovskii functional (LKF) is constructed to obtain the less conservative stability results. Then, in order to cooperate with the introduced LKF, the free-matrix-based inequality (FMBI) is employed in the estimation of the integral quadratic terms. Next, by utilizing the new negative definite conditions (NDCs) of matrix-valued cubic polynomials, the stability conditions are presented in the form of linear matrix inequalities (LMIs). In addition, in the establishment process of these conditions, no extra state variables are introduced and the positive definite constraint on the LKF is relaxed. Finally, the validity and advantages of the proposed conditions are illustrated with some classical numerical examples.