Improved Stability Analysis of Delayed Neural Networks via a Line Integral Bounding Technique Under General Slope Conditions

ABSTRACT

This article focuses on maximally utilizing information on the general slope conditions in activation functions during the stability analysis of delayed neural networks (DNNs). Firstly, a line integral bounding technique (LIBT) is developed to provide bounds for line integrals of nonlinear functions under general slope conditions. The estimated bounds of the LIBT are tighter than those of the existing bounding technique by considering the non‐zero lower bound of the slope condition, which is validated through geometric interpretation. Secondly, novel double integral Lyapunov‐Krasovskii functionals (LKFs) are proposed to achieve a less conservative stability criterion for DNNs. These proposed LKFs utilize information on the general slope conditions in the activation function of DNNs that was previously overlooked. Lastly, an enhanced stability criterion is derived via the novel LKFs and the LIBT, and the reduced conservatism of the obtained criterion is evaluated through representative examples.