发表机构
University of Michigan（密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出渐近稳定性的分级方法，给出相关Lyapunov检验与认证条件，通过多类示例说明该分级可识别主导稳定机制，弥补经典渐近稳定性未量化收敛速率的不足。
AI 中文摘要
经典渐近稳定性仅保证收敛性，未量化收敛速率。本文引入渐近稳定性的分级：0级对应指数稳定性，m>0级对应阶为t^(-1/m)的代数衰减。我们给出可接受分级的直接与逆Lyapunov检验、精确稳定性分级的认证条件。Hopf、Bautin、分数阶及时变示例展示该分级如何识别主导稳定机制。
英文摘要
Classical asymptotic stability guarantees convergence but does not quantify the rate at which convergence occurs. This paper introduces a gradation of asymptotic stability where degree zero corresponds to exponential stability and degree $m>0$ corresponds to algebraic decay of order $t^{-1/m}$. We provide direct and converse Lyapunov characterizations for admissible degrees and conditions for certifying the exact stability degree. Hopf, Bautin, fractional-degree, and time-varying examples demonstrate how the degree identifies the leading stabilizing mechanism.
Comments14 pages, 2 figures
