Improved Stability Criteria for Delayed Neural Networks via Time-Varying Free-Weighting Matrices and S-Procedure

Xi‐Zi Zhou, Jianqi An, Yong He, Jianhua Shen

2023IEEE Transactions on Neural Networks and Learning Systems46 citationsDOI

Abstract

This brief investigates the stability of neural networks with time-varying delays. Novel stability conditions are derived by employing free-matrix-based inequality and introducing the variable-augmented-based free-weighting matrices in the estimation of the derivative of the Lyapunov-Krasovskii functionals (LKFs). Both techniques avoid the appearance of the nonlinear terms of the time-varying delay. Especially, the time-varying free-weighting matrices associated with the derivative of the delay and the time-varying S-Procedure related to the delay and its derivative are combined to improve the presented criteria. Finally, numerical examples are given to illustrate the benefits of the presented methods.

Topics & Concepts

WeightingStability (learning theory)Derivative (finance)Time derivativeArtificial neural networkControl theory (sociology)Variable (mathematics)Computer scienceMathematicsNonlinear systemMatrix (chemical analysis)Mathematical optimizationApplied mathematicsArtificial intelligenceMathematical analysisMachine learningFinancial economicsEconomicsRadiologyQuantum mechanicsComposite materialControl (management)MedicineMaterials sciencePhysicsNeural Networks Stability and SynchronizationStability and Control of Uncertain SystemsMatrix Theory and Algorithms