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arXiv · 2603.22802

Equivalence of Finite- and Fixed-time Stability to Asymptotic Stability

Kunal Garg
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Abstract

In this paper, we present new results on finite- and fixed-time convergence for dynamical systems using LaSalle-like invariance principles. In particular, we provide first and second-order non-smooth Lyapunov-like results for finite- and fixed-time convergence, thereby relaxing the requirement of existence a differentiable, positive definite Lyapunov function. Based on these findings, we show that a dynamical system whose equilibrium point is globally asymptotically stable can be modified through scaling so that the resulting dynamical system has a fixed-time stable equilibrium point. The results in this paper expand our understanding of various convergence rates and strengthen the hypothesis that all the convergence rates are interconnected through a suitable transformation.

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Kunal Garg. 2026-03-24. Equivalence of Finite- and Fixed-time Stability to Asymptotic Stability. https://arxiv.org/abs/2603.22802

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