An operator theoretic approach to infinite‐dimensional control systems

Jacob, Birgit; Zwart, Hans

doi:10.1002/gamm.201800010

Cited by 11 publications

(9 citation statements)

References 29 publications

(85 reference statements)

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“…where ζ ∈ [0, 1] and t ≥ 0, the n × n Hermitian matrix The function x denotes the state of the system, u the input function and y the output of the system. For more information we refer to [11], [12].…”

Section: Problem Statement and Main Resultsmentioning

confidence: 99%

“…This section is devoted to the proof of Theorem 3.1 and we denote by A the operator given by ( 13)-( 14). Again we consider the port-Hamiltonian system ( 9)- (12). Recall that for every intial condition x 0 ∈ D(A) the port-Hamiltonian system ( 9)-( 12) has a unique classical solution.…”

Section: Proof Of Theorem 31mentioning

confidence: 99%

“…We refer to Section III for the precise assumptions on P 1 , G 0 , W B,1 W B,0 , W C,1 W C,0 and H. This class of systems describes a special class of port-Hamiltonian systems, which however is rich enough to cover in particular the wave equation, the transport equation and the Timoshenko beam equation, and also coupled beam and wave equations. For more information on this class of port-Hamiltonian systems we refer to the first paper on this topic, [15], the monograph [11] and the survey [12].…”

Section: Introductionmentioning

confidence: 99%

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Observability for port-Hamiltonian systems

Jacob¹,

Zwart²

2021

Preprint

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The class of port-Hamiltonian systems incorporates many physical models, such as mechanical systems in the finite-dimensional case and wave and beam equations in the infinite-dimensional case. In this paper we study a subclass of linear first order port-Hamiltonian systems. In [3], it is shown that these systems are exactly observable when the energy is not dissipated internally and when sufficient observations are made at the boundary. In this article we study the observability properties for these systems when internal dissipation of energy is possible. We cannot show the exact observability, but we do show that the Hautus test is satisfied. In general, the Hautus test is weaker than exact observability, but stronger than approximate observability. Hence we conclude that these systems are approximately observable.

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Section: Problem Statement and Main Resultsmentioning

confidence: 99%

Section: Proof Of Theorem 31mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Observability for port-Hamiltonian systems

Jacob¹,

Zwart²

2021

Preprint

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“…This result has been instrumental to handle more general systems of coupled PDEs and ODEs and as result repetitive control systems (Califano et al, 2017; have been cast in this rigorous framework to derive novel stability conditions. In Jacob & Zwart (2018) the operator based analysis to dpH systems is extended to address control theoretic properties like controllability and input-to-state stability. It is also important to cite the PhD thesis of Augner (2018), where some stability results for the second order case are present.…”

Section: Well-posedness Stabilization and Control Of Dph Systems As Bcsmentioning

confidence: 99%

Twenty years of distributed port-Hamiltonian systems: a literature review

Rashad

Califano

Schaft

2020

IMA Journal of Mathematical Control and Information

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The port-Hamiltonian (pH) theory for distributed parameter systems has developed greatly in the past two decades. The theory has been successfully extended from finite-dimensional to infinite-dimensional systems through a lot of research efforts. This article collects the different research studies carried out for distributed pH systems. We classify over a hundred and fifty studies based on different research focuses ranging from modeling, discretization, control and theoretical foundations. This literature review highlights the wide applicability of the pH systems theory to complex systems with multi-physical domains using the same tools and language. We also supplement this article with a bibliographical database including all papers reviewed in this paper classified in their respective groups.

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“…It has since then triggered manifold research and ideas. For this we refer to [9,21,2,18,23] and the references therein, see also [8] for a survey. The basic idea is to describe a physical -mostly energy conserving or at least energy dissipating -phenomenon in terms of a partial differential equation in the underlying physical domain together with suitable boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Characterisation for Exponential Stability of port-Hamiltonian Systems

Trostorff¹,

Waurick²

2022

Preprint

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Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density H. In passing, we obtain generalisations for sufficient criteria in the literature by making regularity requirements for the Hamiltonian density largely obsolete. The key assumption for the characterisation (and thus the sufficient critera) to work is a uniform bound for a family of fundamental solutions for some non-autonomous, finite-dimensional ODEs. Regularity conditions on H for previously known criteria such as bounded variation are shown to imply the key assumption. Exponentially stable port-Hamiltonian systems with irregular L ∞ -densities are provided.

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An operator theoretic approach to infinite‐dimensional control systems

Cited by 11 publications

References 29 publications

Observability for port-Hamiltonian systems

Observability for port-Hamiltonian systems

Twenty years of distributed port-Hamiltonian systems: a literature review

Characterisation for Exponential Stability of port-Hamiltonian Systems

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