Improved reciprocally convex cubic matrix inequalities for neural networks with time-varying delay

Abstract

This paper addresses the exponential stability of global neural networks(NNs) systems with time-varying delay. The novel Lyapunov-Krasovskii functionals (LKFs) are proposed, whose derivative is estimated by using the proposed cubic function negative-definiteness condition (NDC). To enhance the interaction between integral inequalities and the NDC for cubic functions, a new reciprocally cubic convex matrix inequality (RCCMI) with parameter dependence is developed, improving the accuracy of the LKFs derivative. Based on the proposed delay-product-dependent LKFs and the developed RCCMI, a less conservative exponential stability criterion is obtained by cubic function NDC. The effectiveness and advantages of the proposed RCCMI are demonstrated through three numerical examples, showing superiority compared to existing approaches.