Expanded Lyapunov-Krasovskii Functionals and Stability Analysis in Delayed Neural Networks via Augmented Zero Equality Approach

This paper proposes improved Lyapunov-Krasovskii functionals (LKFs) for asymptotic stability of generalized neural networks (GNNs) with time-varying delays. By utilizing generalized free-weighting matrix inequality (GFWMI) and some mathematical techniques, sufficient conditions which are dependent on the size of time delays are derived for guaranteeing the stability of GNNs. Additionally, the augmented zero equality approach (AZEA) is applied to enhance the results and eliminate the free variables. Three numerical examples show that the proposed method can be effective and provide less conservative results than previous researches.

Automated summary

This paper proposes improved Lyapunov-Krasovskii functionals (LKFs) for asymptotic stability of generalized neural networks (GNNs) with time-varying delays. Utilizing generalized free-weighting matrix inequality (GFWMI) and mathematical techniques, sufficient conditions dependent on the size of time delays are derived to guarantee the stability of GNNs. The augmented zero equality approach (AZEA) is applied to enhance the results and eliminate free variables. Three numerical examples demonstrate the effectiveness and less conservative results of the proposed method compared to previous research.