Title data
Mironchenko, Andrii ; Schwenninger, Felix:
Coercive quadratic ISS Lyapunov functions for analytic systems.
In:
2023 62nd IEEE Conference on Decision and Control (CDC) : Proceedings. -
Piscataway, NJ, USA
: IEEE
,
2023
. - pp. 4699-4704
ISBN 979-8-3503-0124-3
DOI: https://doi.org/10.1109/CDC49753.2023.10384024
Project information
Project title: |
Project's official title Project's id Lyapunov theory meets boundary control systems MI 1886/2-2 |
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Project financing: |
Deutsche Forschungsgemeinschaft |
Abstract in another language
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 $L^2$-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.
Further data
Item Type: | Article in a book |
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Refereed: | Yes |
Keywords: | infinite-dimensional systems; linear systems; input-to-state stability; Lyapunov methods; semigroup theory |
Subject classification: | Mathematics Subject Classification Code: 37C75 93C25 93D09 |
Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Profile Fields > Advanced Fields > Nonlinear Dynamics |
Result of work at the UBT: | No |
DDC Subjects: | 500 Science > 510 Mathematics |
Date Deposited: | 06 Mar 2025 12:13 |
Last Modified: | 06 Mar 2025 12:13 |
URI: | https://eref.uni-bayreuth.de/id/eprint/92673 |