Publications

@article{WijnTren24a,

title = {Impulse-controllability of system classes of switched differential algebraic equations},

author = {Paul Wijnbergen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2022/08/Preprint-WT220806.pdf, Preprint},

doi = {10.1007/s00498-023-00367-0},

year  = {2024},

date = {2024-06-01},

urldate = {2024-06-01},

journal = {Mathematics of Control, Signals, and Systems},

volume = {36},

issue = {2},

pages = {351–380},

abstract = {In this paper impulse controllability of system classes containing switched DAEs is studied. We introduce several notions of impulse-controllability of system classes and provide a characterization of strong impulse-controllability of system classes generated by arbitrary switching signals. In the case of a system class generated by switching signals with a fixed mode sequence it is shown that either all or almost all systems are impulse-controllable, or that all or almost all systems are impulse-uncontrollable. Sufficient conditions for all systems to be impulse-controllable or impulse-uncontrollable are presented. Furthermore, it is observed that although all systems are impulse-controllable, the input achieving impulse-free solutions might still depend on the switching times in the future, which causes some causality issues. Therefore, the concept of (quasi-) causal impulse-controllability is introduced and system classes which are (quasi-) causal are characterized. Finally necessary and sufficient conditions for a system class to be causal given some dwell-time are stated.},

note = {open access},

keywords = {controllability, DAEs, piecewise-smooth-distributions, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {article}

}

@article{HossTren24,

title = {Midpoint based balanced truncation for switched linear systems with known switching signal},

author = {Sumon Hossain and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2023/05/Preprint-HT230508.pdf, Preprint},

doi = {10.1109/TAC.2023.3269721},

year  = {2024},

date = {2024-01-01},

urldate = {2024-01-01},

journal = {IEEE Transactions on Automatic Control},

volume = {69},

number = {1},

pages = {535-542},

abstract = {We propose a novel model reduction approach for switched linear systems with known switching signal. The class of considered systems encompasses switched systems with mode-dependent state-dimension as well as impulsive systems. Our method is based on a suitable definition of (time-varying) reachability and observability Gramians and we show that these Gramians satisfy precise interpretations in terms of input and output energy. Based on balancing the midpoint Gramians, we propose a piecewise-constant projection based model reduction resulting in a switched linear system of smaller size.},

keywords = {controllability, model-reduction, observability, switched-systems},

pubstate = {published},

tppubtype = {article}

}

@article{HossTren23a,

title = {Reduced realization for switched linear systems with known mode sequence},

author = {Sumon Hossain and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2024/02/HossTren23a.pdf, Paper

https://doi.org/10.5281/zenodo.6410136, Matlab sources},

doi = {10.1016/j.automatica.2023.111065},

year  = {2023},

date = {2023-08-01},

urldate = {2023-08-01},

journal = {Automatica},

volume = {154},

number = {111065},

pages = {1-9},

abstract = {We consider switched linear systems with mode-dependent state-dimensions and/or state jumps and propose a method to obtain a switched system of reduced size with identical input-output behavior. Our approach is based in considering time-dependent reachability and unobservability spaces as well as suitable extended reachability and restricted unobservability spaces together with the notion of a weak Kalman decomposition. A key feature of our approach is that only the mode sequence of the switching signal needs to be known and not the exact switching times. However, the size of a minimal realization will in general depend on the mode durations, hence it cannot be expected that our method always leads to minimal realization. Nevertheless, we show that our method is optimal in the sense that a repeated application doesn’t lead to a further reduction and we also highlight a practically relevant special case, where minimality is achieved.},

note = {open access},

keywords = {controllability, model-reduction, observability, switched-systems},

pubstate = {published},

tppubtype = {article}

}

@article{BergIlch22,

title = {Quasi feedback forms for differential-algebraic systems},

author = {Thomas Berger and Achim Ilchmann and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2023/01/BergIlch22.pdf, Paper

https://arxiv.org/abs/2102.12713, arXiv:2102.12713},

doi = {10.1093/imamci/dnab030},

year  = {2022},

date = {2022-06-01},

urldate = {2022-06-01},

journal = {IMA Journal of Mathematical Control and Information},

volume = {39},

issue = {2},

pages = {533-563},

abstract = {We investigate feedback forms for linear time-invariant systems described by differential-algebraic equations. Feedback forms are representatives of certain equivalence classes. For example state space transformations, invertible transformations from the left, and proportional state feedback constitute an equivalence relation. The representative of such an equivalence class, which we call proportional feedback form for the above example, allows to read off relevant system theoretic properties. Our main contribution is to derive a quasi proportional feedback form. This form is advantageous since it provides some geometric insight and is simple to compute, but still allows to read off the relevant structural properties of the control system. We also derive a quasi proportional and derivative feedback form. Similar advantages hold.},

note = {open access, published online October 2021},

keywords = {controllability, DAEs, normal-forms},

pubstate = {published},

tppubtype = {article}

}

@article{WijnTren21a,

title = {Impulse-free interval-stabilization of switched differential algebraic equations},

author = {Paul Wijnbergen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2021/01/24-SCL149-104870.pdf, Paper},

doi = {10.1016/j.sysconle.2020.104870},

year  = {2021},

date = {2021-01-23},

urldate = {2021-01-23},

journal = {Systems & Control Letters},

volume = {149},

pages = {104870.1-10},

abstract = {In this paper stabilization of switched differential algebraic equations is considered, where Dirac impulses in both the input and the state trajectory are to be avoided during the stabilization process. First it is shown that stabilizability of a switched DAE and the existence of impulse-free solutions are merely necessary conditions for impulse-free stabilizability. Then necessary and sufficient conditions for the existence of impulse-free solutions are given, which motivate the definition of (impulse-free) interval-stabilization on a finite interval. Under a uniformity assumption, which can be verified for a broad class of switched systems, stabilizability on an infinite interval can be concluded based on interval-stabilizability. As a result a characterization of impulse-free interval stabilizability is given and as a corollary we provide a novel impulse-free null-controllability characterization. Finally, the results are compared to results on interval-stabilizability where Dirac impulses are allowed in the input and state trajectory.

},

note = {Open Access.},

keywords = {controllability, piecewise-smooth-distributions, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {article}

}

@article{KustTren16a,

title = {Duality of switched DAEs},

author = {Ferdinand Küsters and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KT160627.pdf, Preprint},

doi = {10.1007/s00498-016-0177-2},

year  = {2016},

date = {2016-07-01},

journal = {Math. Control Signals Syst.},

volume = {28},

number = {3},

pages = {25},

abstract = {We present and discuss the definition of the adjoint and dual of a switched differential-algebraic equation (DAE). For a proper duality definition, it is necessary to extend the class of switched DAEs to allow for additional impact terms. For this switched DAE with impacts, we derive controllability/reachability/determinability/observability characterizations for a given switching signal. Based on this characterizations, we prove duality between controllability/reachability and determinability/observability for switched DAEs.},

keywords = {controllability, DAEs, observability, piecewise-smooth-distributions, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {article}

}

@article{KustRupp15,

title = {Controllability of switched differential-algebraic equations},

author = {Ferdinand Küsters and Markus G.-M. Ruppert and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KRT150122.pdf, Preprint},

doi = {10.1016/j.sysconle.2015.01.011},

issn = {0167-6911},

year  = {2015},

date = {2015-01-01},

journal = {Syst. Control Lett.},

volume = {78},

number = {0},

pages = {32 - 39},

abstract = {We study controllability of switched differential–algebraic equations. We are able to establish a controllability characterization where we assume that the switching signal is known. The characterization takes into account possible jumps induced by the switches. It turns out that controllability not only depends on the actual switching sequence but also on the duration between the switching times.},

keywords = {controllability, DAEs, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {article}

}

@article{BergTren14,

title = {Kalman controllability decompositions for differential-algebraic systems},

author = {Thomas Berger and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-BT140603.pdf, Preprint},

doi = {10.1016/j.sysconle.2014.06.004},

issn = {0167-6911},

year  = {2014},

date = {2014-01-01},

journal = {Syst. Control Lett.},

volume = {71},

pages = {54--61},

abstract = {We study linear differential-algebraic control systems and investigate decompositions with respect to controllability properties. We show that the augmented Wong sequences can be exploited for a transformation of the system into a Kalman controllability decomposition (KCD). The KCD decouples the system into a completely controllable part, an uncontrollable part given by an ordinary differential equation and an inconsistent part, which is behaviorally controllable but contains no completely controllable part. This decomposition improves a known KCD from a behavioral point of view. We conclude the paper with some features of the KCD in the case of regular systems.},

keywords = {controllability, DAEs, normal-forms},

pubstate = {published},

tppubtype = {article}

}

@article{Tren09a,

title = {A normal form for pure differential algebraic systems},

author = {Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-Tre081215.pdf, Preprint},

doi = {10.1016/j.laa.2008.10.004},

year  = {2009},

date = {2009-01-01},

journal = {Linear Algebra Appl.},

volume = {430},

number = {4},

pages = {1070 -- 1084},

abstract = {In this paper linear time-invariant differential algebraic equations (DAEs) are studied; the focus is on pure DAEs which are DAEs without an ordinary differential equation (ODE) part. A normal form for pure DAEs is given which is similar to the Byrnes–Isidori normal form for ODEs. Furthermore, the normal form exhibits a Kalman-like decomposition into impulse-controllable- and impulse-observable states. This leads to a characterization of impulse-controllability and observability.},

keywords = {controllability, DAEs, normal-forms, observability, relative-degree},

pubstate = {published},

tppubtype = {article}

}