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). @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 = {DAEs, delay, networks, open-access, PDEs, piecewise-smooth-distributions, solution-theory, switched-DAEs},
pubstate = {published},
tppubtype = {article}
}
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. |

Trenn, Stephan; Unger, Benjamin Delay regularity of differential-algebraic equations Inproceedings In: Proc. 58th IEEE Conf. Decision Control (CDC) 2019, pp. 989-994, Nice, France, 2019. @inproceedings{TrenUnge19,
title = {Delay regularity of differential-algebraic equations},
author = {Stephan Trenn and Benjamin Unger},
url = {https://stephantrenn.net/wp-content/uploads/2019/03/Preprint-TU190910.pdf, Preprint},
doi = {10.1109/CDC40024.2019.9030146},
year = {2019},
date = {2019-12-12},
booktitle = {Proc. 58th IEEE Conf. Decision Control (CDC) 2019},
pages = {989-994},
address = {Nice, France},
abstract = {We study linear time-invariant delay differential-algebraic equations (DDAEs). Such equations can arise if a feedback controller is applied to a descriptor system and the controller requires some time to measure the state and to compute the feedback resulting in the time-delay. We present an existence and uniqueness result for DDAEs within the space of piecewise-smooth distributions and an algorithm to determine whether a DDAE is delay-regular.},
keywords = {CDC, DAEs, delay, solution-theory},
pubstate = {published},
tppubtype = {inproceedings}
}
We study linear time-invariant delay differential-algebraic equations (DDAEs). Such equations can arise if a feedback controller is applied to a descriptor system and the controller requires some time to measure the state and to compute the feedback resulting in the time-delay. We present an existence and uniqueness result for DDAEs within the space of piecewise-smooth distributions and an algorithm to determine whether a DDAE is delay-regular. |