Improved Stability Criteria for Delayed Neural Networks: Further Utilization of Information on Time-Varying Delays and Activation Functions
本文针对时滞神经网络，通过引入时滞乘积项和激活函数相关项，提出了新的稳定性判据，降低了保守性，并通过两个典型例子验证了方法的优势。
This article focuses on the low-conservative stability criteria of delayed neural networks (DNNs). To achieve this goal, new techniques are developed to effectively utilize more system-related information. To use the time-varying delay information, some delay-product terms are introduced into the Lyapunov-Krasovskii functional (LKF), and an extended matrix-injection-based transformation method, which introduces delay-derivative-dependent slack matrices while obtaining the negative definite condition, is proposed. With respect to the use of activation function information, the terms related to the activation function are fully augmented in the LKF. In particular, by considering the sector-constraint information of the activation function, a new nonlinear-function-dependent functional term is established, and a sector-constraint-dependent matrix-separation-based inequality is developed. By applying the above techniques, several improved stability criteria are derived, and two typical examples are provided to illustrate the advantages of the proposed methods.