Improved Passivity Analysis for Neural Networks With Time-Varying Delay
本文提出一种线性化变量增广方法和改进的时变S过程，消除了非线性延迟项，得到了比现有结果保守性更低的神经网络无源性和稳定性判据，并通过数值例子和实际案例验证。
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.