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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.22786 |
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| _version_ | 1866918264574050304 |
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| author | Bingöl, Özhan |
| author_facet | Bingöl, Özhan |
| contents | Predefined-time stability enables convergence within a user-specified time independent of initial conditions. Existing results are predominantly based on autonomous Lyapunov inequalities, where the predefined-time is realized through integral bounds on state-dependent decay and therefore acts as an upper bound rather than a structurally enforced deadline. This paper introduces a time-barrier predefined-time stability concept in which convergence is enforced through a nonautonomous Lyapunov mechanism that intrinsically restricts the remaining available time. A sufficient Lyapunov-based condition is established, guaranteeing convergence before the predefined deadline via divergence of a time-dependent barrier. It is further shown that this mechanism cannot be reproduced by classical autonomous predefined-time stability formulations, thereby constituting a distinct stability notion. The proposed approach provides a concise and transparent means of enforcing hard convergence deadlines in nonlinear systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22786 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Time-Barrier Lyapunov Condition for Predefined-Time Stability Bingöl, Özhan Systems and Control Predefined-time stability enables convergence within a user-specified time independent of initial conditions. Existing results are predominantly based on autonomous Lyapunov inequalities, where the predefined-time is realized through integral bounds on state-dependent decay and therefore acts as an upper bound rather than a structurally enforced deadline. This paper introduces a time-barrier predefined-time stability concept in which convergence is enforced through a nonautonomous Lyapunov mechanism that intrinsically restricts the remaining available time. A sufficient Lyapunov-based condition is established, guaranteeing convergence before the predefined deadline via divergence of a time-dependent barrier. It is further shown that this mechanism cannot be reproduced by classical autonomous predefined-time stability formulations, thereby constituting a distinct stability notion. The proposed approach provides a concise and transparent means of enforcing hard convergence deadlines in nonlinear systems. |
| title | A Time-Barrier Lyapunov Condition for Predefined-Time Stability |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2512.22786 |