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Stephan Trenn

Stephan Trenn

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Month: December 2019

Posted on 2019-12-122019-12-12

Slides of my CDC talk online

The slides of my CDC talk “The one-step-map for switched singular systems in discrete-time” are now available on my Talks site.

Posted on 2019-12-062019-12-06

Paper on PDEs coupled to swDAEs submitted

Finally we have published our key theoretical paper four our DFG-project “Coupling hyperbolic PDEs with switched DAEs: Analysis, numerics and application to blood flow models”:

Borsche, Raul; Kocoglu, Damla; Trenn, Stephan

A distributional solution framework for linear hyperbolic PDEs coupled to switched DAEs Journal Article

In: Mathematics of Control, Signals, and Systems (MCSS), vol. 32, pp. 455-487, 2020, (Open Access).

Abstract | Links | BibTeX

@article{BorsKoco20,
title = {A distributional solution framework for linear hyperbolic PDEs coupled to switched DAEs},
author = {Raul Borsche and Damla Kocoglu and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2020/11/23-MCSS2020.pdf, Paper},
doi = {10.1007/s00498-020-00267-7},
year = {2020},
date = {2020-11-18},
urldate = {2020-11-18},
journal = {Mathematics of Control, Signals, and Systems (MCSS)},
volume = {32},
pages = {455-487},
abstract = {A distributional solution framework is developed for systems consisting of linear hyperbolic partial differential equations (PDEs) and switched differential-algebraic equations (DAEs) which are coupled via boundary conditions. The unique solvability is then characterize in terms of a switched delay DAE. The theory is illustrated with an example of electric power lines modeled by the telegraph equations which are coupled via a switching transformer where simulations confirm the predicted impulsive solutions.},
note = {Open Access},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

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A distributional solution framework is developed for systems consisting of linear hyperbolic partial differential equations (PDEs) and switched differential-algebraic equations (DAEs) which are coupled via boundary conditions. The unique solvability is then characterize in terms of a switched delay DAE. The theory is illustrated with an example of electric power lines modeled by the telegraph equations which are coupled via a switching transformer where simulations confirm the predicted impulsive solutions.

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  • Paper
  • doi:10.1007/s00498-020-00267-7

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In this paper, we provide a novel distributional solution framework to handle jumps and Dirac impulses on the boundaries of the domain of a hyperbolic PDE. It also includes a nice example of electrical power lines (modeled via the telegraph equation) with a switching transformer (modeled by a switched DAE). The simulations nicely show how a Dirac impulse (induced by a switch) is moving through time and space as predicted by the theory.

Posted on 2019-12-062019-12-06

Two submission to IFAC WC ’20

Together with my PhD-students we have prepared the following two submission to the IFAC World Congress 2020 to be held in Berlin next year:

Wijnbergen, Paul; Jeeninga, Mark; Trenn, Stephan

On stabilizability of switched differential algebraic equations Proceedings Article

In: IFAC-PapersOnLine 53-2, pp. 4304-4309, 2020, (Proc. IFAC World Congress 2020, Berlin, Germany. Open access.).

Abstract | Links | BibTeX

@inproceedings{WijnJeen20,
title = {On stabilizability of switched differential algebraic equations},
author = {Paul Wijnbergen and Mark Jeeninga and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2021/06/WijnJeen20.pdf, Paper},
doi = {10.1016/j.ifacol.2020.12.2580},
year = {2020},
date = {2020-07-06},
booktitle = {IFAC-PapersOnLine 53-2},
pages = {4304-4309},
abstract = {This paper considers stabilizability of switched differential algebraic equations (DAEs). We first introduce the notion of interval stabilizability and show that under a certain uniformity assumption, stabilizability can be concluded from interval stabilizability. A geometric approach is taken to find necessary and sufficient conditions for interval stabilizability. This geometric approach can also be utilized to derive a novel characterization of controllability.},
note = {Proc. IFAC World Congress 2020, Berlin, Germany. Open access.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}

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This paper considers stabilizability of switched differential algebraic equations (DAEs). We first introduce the notion of interval stabilizability and show that under a certain uniformity assumption, stabilizability can be concluded from interval stabilizability. A geometric approach is taken to find necessary and sufficient conditions for interval stabilizability. This geometric approach can also be utilized to derive a novel characterization of controllability.

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  • Paper
  • doi:10.1016/j.ifacol.2020.12.2580

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Hossain, Sumon; Trenn, Stephan

A time-varying Gramian based model reduction approach for Linear Switched Systems Proceedings Article

In: IFAC PapersOnline 53-2, pp. 5629-5634, 2020, (Proc. IFAC World Congress 2020, Berlin, Germany. Open access.).

Abstract | Links | BibTeX

@inproceedings{HossTren20a,
title = {A time-varying Gramian based model reduction approach for Linear Switched Systems},
author = {Sumon Hossain and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2021/06/HossTren20a.pdf, Paper (open access)},
doi = {10.1016/j.ifacol.2020.12.1580},
year = {2020},
date = {2020-07-05},
urldate = {2020-07-05},
booktitle = {IFAC PapersOnline 53-2},
pages = {5629-5634},
abstract = {We propose a model reduction approach for switched linear system based on a balanced truncation reduction method for linear time-varying systems. The key idea is to approximate the piecewise-constant coefficient matrices with continuous time-varying coefficients and then apply available balance truncation methods for (continuous) time-varying systems. The proposed method is illustrated with a low dimensional academic example.},
note = {Proc. IFAC World Congress 2020, Berlin, Germany. Open access.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}

Close

We propose a model reduction approach for switched linear system based on a balanced truncation reduction method for linear time-varying systems. The key idea is to approximate the piecewise-constant coefficient matrices with continuous time-varying coefficients and then apply available balance truncation methods for (continuous) time-varying systems. The proposed method is illustrated with a low dimensional academic example.

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  • Paper (open access)
  • doi:10.1016/j.ifacol.2020.12.1580

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