Abstract
We investigate the relationship between input-to-state stability (ISS) of linear infinite-dimensional systems and existence of coercive ISS Lyapunov functions. We show that input-to-state stability of a linear system does not imply existence of a coercive quadratic ISS Lyapunov function, even if the underlying semigroup is analytic, and the input operator is bounded. However, if in addition the semigroup is similar to a contraction semigroup on a Hilbert space, then a quadratic ISS Lyapunov function always exists. Next we consider analytic and similar to contraction semi-groups in Hilbert spaces with unbounded input operator B. If B is slightly stronger than 2-admissible, we construct explicitly a coercive L2-ISS Lyapunov function. If the generator of a semigroup is additionally self-adjoint, this Lyapunov function is precisely a square norm in the state space.
| Original language | English |
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| Title of host publication | 2023 62nd IEEE Conference on Decision and Control, CDC 2023 |
| Place of Publication | Piscataway, NJ |
| Publisher | IEEE |
| Pages | 4699-4704 |
| Number of pages | 6 |
| ISBN (Electronic) | 979-8-3503-0124-3, 979-8-3503-0123-6 (USB) |
| ISBN (Print) | 979-8-3503-0125-0 |
| DOIs | |
| Publication status | Published - 2023 |
| Event | 62nd IEEE Conference on Decision and Control, CDC 2023 - Singapore, Singapore Duration: 13 Dec 2023 → 15 Dec 2023 Conference number: 62 |
Publication series
| Name | Proceedings of the IEEE Conference on Decision and Control (CDC) |
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| Publisher | IEEE |
| Number | 62 |
| Volume | 2023 |
| ISSN (Print) | 0743-1546 |
| ISSN (Electronic) | 2576-2370 |
Conference
| Conference | 62nd IEEE Conference on Decision and Control, CDC 2023 |
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| Abbreviated title | CDC 2023 |
| Country/Territory | Singapore |
| City | Singapore |
| Period | 13/12/23 → 15/12/23 |
Keywords
- Infinite-dimensional systems
- Input-to-state stability
- Linear systems
- Lyapunov methods
- Semigroup theory
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