On BIBO stability of infinite-dimensional linear state space systems

Alexander A. Wierzba

On BIBO stability of infinite-dimensional linear state space systems

Mathematical Systems Theory

Research output: Contribution to conference › Poster › Academic

Abstract

In this contribution we consider bounded-input-bounded-output (BIBO) stability of systems described by infinite-dimensional linear state-space representations. In line with classical approaches to infinite-dimensional systems, we use tools from operator theory (semigroups, system nodes) to fill the so far unattended gap of a formal definition and characterization of BIBO stability in this general case.
Furthermore, we provide several sufficient conditions guaranteeing BIBO stability and discuss to which extent this property is preserved under additive and multiplicative perturbations of the associated semigroup generator.
This contribution is based upon joint work with Felix L. Schwenninger and Hans Zwart. The preprint is available at https://arxiv.org/abs/2303.18148.

Original language	English
Publication status	Published - 27 Sept 2023
Event	4th Workshop on Stability and Control of Infinite-Dimensional Systems, SCINDIS 2023 - Bergische Universität Wuppertal, Wuppertal, Germany Duration: 27 Oct 2022 → 29 Oct 2022 Conference number: 4

Workshop

Workshop	4th Workshop on Stability and Control of Infinite-Dimensional Systems, SCINDIS 2023
Abbreviated title	SCINDIS 2023
Country/Territory	Germany
City	Wuppertal
Period	27/10/22 → 29/10/22

1 Article

On BIBO stability of infinite-dimensional linear state-space systems
Schwenninger, F. L., Wierzba, A. A. & Zwart, H., 1 Jan 2024, In: SIAM journal on control and optimization. 62, 1, p. 22-41 20 p.
Research output: Contribution to journal › Article › Academic › peer-review

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Cite this

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title = "On BIBO stability of infinite-dimensional linear state space systems",

abstract = "In this contribution we consider bounded-input-bounded-output (BIBO) stability of systems described by infinite-dimensional linear state-space representations. In line with classical approaches to infinite-dimensional systems, we use tools from operator theory (semigroups, system nodes) to fill the so far unattended gap of a formal definition and characterization of BIBO stability in this general case.Furthermore, we provide several sufficient conditions guaranteeing BIBO stability and discuss to which extent this property is preserved under additive and multiplicative perturbations of the associated semigroup generator.This contribution is based upon joint work with Felix L. Schwenninger and Hans Zwart. The preprint is available at https://arxiv.org/abs/2303.18148.",

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N2 - In this contribution we consider bounded-input-bounded-output (BIBO) stability of systems described by infinite-dimensional linear state-space representations. In line with classical approaches to infinite-dimensional systems, we use tools from operator theory (semigroups, system nodes) to fill the so far unattended gap of a formal definition and characterization of BIBO stability in this general case.Furthermore, we provide several sufficient conditions guaranteeing BIBO stability and discuss to which extent this property is preserved under additive and multiplicative perturbations of the associated semigroup generator.This contribution is based upon joint work with Felix L. Schwenninger and Hans Zwart. The preprint is available at https://arxiv.org/abs/2303.18148.

AB - In this contribution we consider bounded-input-bounded-output (BIBO) stability of systems described by infinite-dimensional linear state-space representations. In line with classical approaches to infinite-dimensional systems, we use tools from operator theory (semigroups, system nodes) to fill the so far unattended gap of a formal definition and characterization of BIBO stability in this general case.Furthermore, we provide several sufficient conditions guaranteeing BIBO stability and discuss to which extent this property is preserved under additive and multiplicative perturbations of the associated semigroup generator.This contribution is based upon joint work with Felix L. Schwenninger and Hans Zwart. The preprint is available at https://arxiv.org/abs/2303.18148.

M3 - Poster

T2 - 4th Workshop on Stability and Control of Infinite-Dimensional Systems, SCINDIS 2023

Y2 - 27 October 2022 through 29 October 2022

ER -

On BIBO stability of infinite-dimensional linear state space systems

Abstract

Workshop

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Research output

On BIBO stability of infinite-dimensional linear state-space systems

Cite this