A superposition approach for the ISS Lyapunov-Krasovskii theorem with pointwise dissipation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914398270914560 |
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| author | Mironchenko, Andrii Wirth, Fabian Chaillet, Antoine Brivadis, Lucas |
| author_facet | Mironchenko, Andrii Wirth, Fabian Chaillet, Antoine Brivadis, Lucas |
| contents | We show that the existence of a Lyapunov-Krasovskii functional (LKF) with pointwise dissipation (i.e. dissipation in terms of the current solution norm) suffices for input-to-state stability, provided that uniform global stability can also be ensured using the same LKF. To this end, we develop a stability theory, in which the behavior of solutions is not assessed through the classical norm but rather through a specific LKF, which may provide significantly tighter estimates. We discuss the advantages of our approach by means of an example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15346 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A superposition approach for the ISS Lyapunov-Krasovskii theorem with pointwise dissipation Mironchenko, Andrii Wirth, Fabian Chaillet, Antoine Brivadis, Lucas Optimization and Control Systems and Control Dynamical Systems We show that the existence of a Lyapunov-Krasovskii functional (LKF) with pointwise dissipation (i.e. dissipation in terms of the current solution norm) suffices for input-to-state stability, provided that uniform global stability can also be ensured using the same LKF. To this end, we develop a stability theory, in which the behavior of solutions is not assessed through the classical norm but rather through a specific LKF, which may provide significantly tighter estimates. We discuss the advantages of our approach by means of an example. |
| title | A superposition approach for the ISS Lyapunov-Krasovskii theorem with pointwise dissipation |
| topic | Optimization and Control Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2603.15346 |