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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.14057 |
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| _version_ | 1866918161575575552 |
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| author | Heni, Rahma Mironchenko, Andrii Wirth, Fabian Damak, Hanen Hammami, Mohamed Ali |
| author_facet | Heni, Rahma Mironchenko, Andrii Wirth, Fabian Damak, Hanen Hammami, Mohamed Ali |
| contents | We prove that (local) input-to-state stability ((L)ISS) and integral input-to-state stability (iISS) of time-varying infinite-dimensional systems in abstract spaces follows from the existence of a {corresponding} Lyapunov function. In particular, input-to-state stability of linear time-varying control systems in Hilbert spaces with bounded input operators is discussed. Methods for the construction of non-coercive LISS/iISS Lyapunov functions are presented for a certain class of time-varying semi-linear evolution equations. Two examples are given to illustrate the effectiveness of the results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14057 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lyapunov methods for input-to-state stability of time-varying evolution equations Heni, Rahma Mironchenko, Andrii Wirth, Fabian Damak, Hanen Hammami, Mohamed Ali Optimization and Control We prove that (local) input-to-state stability ((L)ISS) and integral input-to-state stability (iISS) of time-varying infinite-dimensional systems in abstract spaces follows from the existence of a {corresponding} Lyapunov function. In particular, input-to-state stability of linear time-varying control systems in Hilbert spaces with bounded input operators is discussed. Methods for the construction of non-coercive LISS/iISS Lyapunov functions are presented for a certain class of time-varying semi-linear evolution equations. Two examples are given to illustrate the effectiveness of the results. |
| title | Lyapunov methods for input-to-state stability of time-varying evolution equations |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.14057 |