Further analysis of weighted integral inequalities for improved exponential stability analysis of time delay neural networks systems

TL;DR

This paper introduces new weighted integral inequalities and Lyapunov-Krasovskii functionals to improve exponential stability analysis of time delay neural networks, especially with time-varying delays, validated by numerical examples.

Contribution

It develops novel weighted integral inequalities and stability criteria for neural networks with time delays, extending existing results and enhancing analysis accuracy.

Findings

New weighted integral inequality for stability analysis

Extended stability criteria for time-varying delays

Validated effectiveness through numerical examples

Abstract

This work investigates the exponential stability of neural networks (NNs) systems with time delays. By considering orthogonal polynomials with weighted terms, a new weighted integral inequality is presented. This inequality extend several recently established results. Additionally, based on the reciprocally convex inequality, this study focuses on analyzing the exponential stability of systems with time-varying delays that include an exponential decay factor, a weighted version of the reciprocally convex inequality is first derived. Utilizing these inequalities and the suitable Lyapunov-Krasovskii functionals (LKFs) within the framework of linear matrix inequalities (LMIs), the new criteria for the exponential stability of NNs system is obtained. The effectiveness of the proposed method is demonstrated through multiple numerical examples.