Hierarchical Stability Conditions for Generalized Neural Networks With Interval Time-Varying Delay

This article studies the stability issue and provides the hierarchical stability conditions for generalized neural networks (GNNs) embedded with interval variant delay (delay’s differential is unidentified). First, by transforming the state vectors with integral in the generalized free-matrix-based integral inequalities (GFIIs) into the multiple integral state vectors, the Lyapunov-Krasovskii functional (LKF) with hierarchy is put up based on these multiple integrals. Then, in the treatment of the LKF derivative, the GFIIs are utilized to estimate the delay related integrals of the quadratic product items. For the LKF differential, it is obtained as the delay function with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2N-1$ </tex-math></inline-formula> degree. Next, to set up the linear matrix inequality (LMI) forms and solve the nonlinear items injected by the GFIIs, the novel matrix-based negative conditions (NCs) for odd degree polynomials are put forward. Finally, the superiority of the proposed stability conditions with hierarchy is illustrated by several numerical examples.