Improved Passivity Analysis for Neural Networks With Time-Varying Delay

This article presents the passivity analysis of neural networks with time-varying delays (NNTVDs). The primary challenge stems from nonlinear delay-dependent terms that arise in estimating the derivative of the Lyapunov-Krasovskii functional (LKF). To address this, a linearization variable augmentation method is developed that strategically employs zero equations in conjunction with time-varying free-weighting matrices incorporating the delay derivative. This novel formulation completely eliminates nonlinear delay terms, rendering the passivity condition affine with respect to the delay. Furthermore, an improved time-varying S-procedure is proposed, where the multiplier matrices are constructed as affine functions of the delay, its derivative, and their product, providing greater freedom for bounding the neuron activation functions. These two key innovations together yield novel passivity and stability criteria that are significantly less conservative than existing ones, as rigorously demonstrated by comparative numerical examples and a practical case study.