Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Narter, Yigit, Incer, Inigo
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208737984
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