Stability Analysis for Delayed Neural Networks via a Generalized Reciprocally Convex Inequality

Hui-Chao Lin, Hong-Bing Zeng, Xian-Ming Zhang, Wei Wang

2022IEEE Transactions on Neural Networks and Learning Systems119 citationsDOI

Abstract

This article deals with the stability of neural networks (NNs) with time-varying delay. First, a generalized reciprocally convex inequality (RCI) is presented, providing a tight bound for reciprocally convex combinations. This inequality includes some existing ones as special case. Second, in order to cater for the use of the generalized RCI, a novel Lyapunov-Krasovskii functional (LKF) is constructed, which includes a generalized delay-product term. Third, based on the generalized RCI and the novel LKF, several stability criteria for the delayed NNs under study are put forward. Finally, two numerical examples are given to illustrate the effectiveness and advantages of the proposed stability criteria.

Topics & Concepts

Stability (learning theory)MathematicsRegular polygonArtificial neural networkLinear matrix inequalityInequalityApplied mathematicsOrder (exchange)Upper and lower boundsConvex combinationStability conditionsConvex functionConvex optimizationJensen's inequalityMathematical optimizationConvex analysisLinear inequalityExponential stabilityControl theory (sociology)Variational inequalityComputer scienceType (biology)Stability criterionNeural Networks Stability and SynchronizationNeural Networks and ApplicationsModel Reduction and Neural Networks