Global Asymptotic Stability for Delayed Neural Networks via High-Degree Reciprocally Convex Inequality
提出高阶倒数凸不等式来估计倒数凸组合的下界，并构造新的Lyapunov-Krasovskii泛函，得到延迟广义神经网络渐近稳定性的保守性更小的判据，通过数值和实际四水箱过程验证了有效性。
This article investigates the stability of delayed generalized neural networks (GNNs). First, a high-degree reciprocally convex inequality (RCI) is introduced, offering a novel method for estimating the lower bound of the reciprocally convex combination (RCC). This high-degree RCI subsumes several representative results as special cases. Second, to leverage the advantages of the high-degree RCI, a new Lyapunov–Krasovskii functional (LKF) in accordance with the application of high-degree RCI of order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r=3$</tex-math> </inline-formula> is constructed. Based on the high-degree RCI and the novel LKF, a less conservative delay-dependent stability criterion is derived to ensure the asymptotic stability of delayed GNNs. Third, four widely adopted numerical examples and a study on a real-world quadruple-tank process have been conducted to demonstrate the validity and merits of the new stability criterion.