Equivalence of Finite- and Fixed-time Stability to Asymptotic Stability
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908909069926400 |
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| author | Garg, Kunal |
| author_facet | Garg, Kunal |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22802 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equivalence of Finite- and Fixed-time Stability to Asymptotic Stability Garg, Kunal Optimization and Control Systems and Control 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. |
| title | Equivalence of Finite- and Fixed-time Stability to Asymptotic Stability |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2603.22802 |