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Coercive quadratic ISS Lyapunov functions for analytic systems

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

Official URL: Volltext

Project information

Project title:
Project's official title
Project's id
Lyapunov theory meets boundary control systems
MI 1886/2-2

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
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