Below you find an interactive list of all my publications, which can be filtered by keywords, year, publication type and coauthors. There are also static lists of my books/book-chapters as well as journal and conference publications.

## 2014 |

Berger, Thomas; Trenn, Stephan Kalman controllability decompositions for differential-algebraic systems Journal Article Syst. Control Lett., 71 , pp. 54–61, 2014, ISSN: 0167-6911. Abstract | Links | BibTeX | Tags: controllability, DAEs, normal-forms @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} } 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. |

## 2013 |

Berger, Thomas; Trenn, Stephan Addition to ``The quasi-Kronecker form for matrix pencils'' Journal Article SIAM J. Matrix Anal. & Appl., 34 (1), pp. 94–101, 2013. Abstract | Links | BibTeX | Tags: DAEs, normal-forms, solution-theory @article{BergTren13, title = {Addition to ``The quasi-Kronecker form for matrix pencils''}, author = {Thomas Berger and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/BergTren13.pdf, Paper}, doi = {10.1137/120883244}, year = {2013}, date = {2013-02-11}, journal = {SIAM J. Matrix Anal. & Appl.}, volume = {34}, number = {1}, pages = {94--101}, abstract = {We refine a result concerning singular matrix pencils and the Wong sequences. In our recent paper [T. Berger and S. Trenn, SIAM J. Matrix Anal. Appl., 33 (2012), pp. 336--368] we have shown that the Wong sequences are sufficient to obtain a quasi-Kronecker form. However, we applied the Wong sequences again on the regular part to decouple the regular matrix pencil corresponding to the finite and infinite eigenvalues. The current paper is an addition to [T. Berger and S. Trenn, SIAM J. Matrix Anal. Appl., 33 (2012), pp. 336--368], which shows that the decoupling of the regular part can be done already with the help of the Wong sequences of the original matrix pencil. Furthermore, we show that the complete Kronecker canonical form can be obtained with the help of the Wong sequences.}, keywords = {DAEs, normal-forms, solution-theory}, pubstate = {published}, tppubtype = {article} } We refine a result concerning singular matrix pencils and the Wong sequences. In our recent paper [T. Berger and S. Trenn, SIAM J. Matrix Anal. Appl., 33 (2012), pp. 336--368] we have shown that the Wong sequences are sufficient to obtain a quasi-Kronecker form. However, we applied the Wong sequences again on the regular part to decouple the regular matrix pencil corresponding to the finite and infinite eigenvalues. The current paper is an addition to [T. Berger and S. Trenn, SIAM J. Matrix Anal. Appl., 33 (2012), pp. 336--368], which shows that the decoupling of the regular part can be done already with the help of the Wong sequences of the original matrix pencil. Furthermore, we show that the complete Kronecker canonical form can be obtained with the help of the Wong sequences. |

## 2012 |

Berger, Thomas; Trenn, Stephan The quasi-Kronecker form for matrix pencils Journal Article SIAM J. Matrix Anal. & Appl., 33 (2), pp. 336–368, 2012. Abstract | Links | BibTeX | Tags: DAEs, normal-forms, solution-theory @article{BergTren12, title = {The quasi-Kronecker form for matrix pencils}, author = {Thomas Berger and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/BergTren12.pdf, Paper}, doi = {10.1137/110826278}, year = {2012}, date = {2012-05-03}, journal = {SIAM J. Matrix Anal. & Appl.}, volume = {33}, number = {2}, pages = {336--368}, abstract = {We study singular matrix pencils and show that the so-called Wong sequences yield a quasi-Kronecker form. This form decouples the matrix pencil into an underdetermined part, a regular part, and an overdetermined part. This decoupling is sufficient to fully characterize the solution behavior of the differential-algebraic equations associated with the matrix pencil. Furthermore, we show that the minimal indices of the pencil can be determined with only the Wong sequences and that the Kronecker canonical form is a simple corollary of our result; hence, in passing, we also provide a new proof for the Kronecker canonical form. The results are illustrated with an example given by a simple electrical circuit.}, keywords = {DAEs, normal-forms, solution-theory}, pubstate = {published}, tppubtype = {article} } We study singular matrix pencils and show that the so-called Wong sequences yield a quasi-Kronecker form. This form decouples the matrix pencil into an underdetermined part, a regular part, and an overdetermined part. This decoupling is sufficient to fully characterize the solution behavior of the differential-algebraic equations associated with the matrix pencil. Furthermore, we show that the minimal indices of the pencil can be determined with only the Wong sequences and that the Kronecker canonical form is a simple corollary of our result; hence, in passing, we also provide a new proof for the Kronecker canonical form. The results are illustrated with an example given by a simple electrical circuit. |

Berger, Thomas; Ilchmann, Achim; Trenn, Stephan The quasi-Weierstraß form for regular matrix pencils Journal Article Linear Algebra Appl., 436 (10), pp. 4052–4069, 2012, (published online February 2010). Abstract | Links | BibTeX | Tags: DAEs, normal-forms, solution-theory @article{BergIlch12a, title = {The quasi-Weierstraß form for regular matrix pencils}, author = {Thomas Berger and Achim Ilchmann and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-BIT091017.pdf, Preprint http://dx.doi.org/10.1016/S0024-3795(11)00688-4, Corrections (see Paragraph 6 of Note to Editors)}, doi = {10.1016/j.laa.2009.12.036}, year = {2012}, date = {2012-01-01}, journal = {Linear Algebra Appl.}, volume = {436}, number = {10}, pages = {4052--4069}, abstract = {Regular linear matrix pencils A- E d in K^{n x n}[d], where K=Q, R or C, and the associated differential algebraic equation (DAE) E x' = A x are studied. The Wong sequences of subspaces are investigate and invoked to decompose the K^n into V* + W*, where any bases of the linear spaces V* and W* transform the matrix pencil into the Quasi-Weierstraß form. The Quasi-Weierstraß form of the matrix pencil decouples the original DAE into the underlying ODE and the pure DAE or, in other words, decouples the set of initial values into the set of consistent initial values V* and ``pure'' inconsistent initial values W* - {0}. Furthermore, V* and W* are spanned by the generalized eigenvectors at the finite and infinite eigenvalues, resp. The Quasi-Weierstraß form is used to show how chains of generalized eigenvectors at finite and infinite eigenvalues of A- E d lead to the well-known Weierstraß form. So the latter can be viewed as a generalized Jordan form. Finally, it is shown how eigenvector chains constitute a basis for the solution space of E x' = A x.}, note = {published online February 2010}, keywords = {DAEs, normal-forms, solution-theory}, pubstate = {published}, tppubtype = {article} } Regular linear matrix pencils A- E d in K^{n x n}[d], where K=Q, R or C, and the associated differential algebraic equation (DAE) E x' = A x are studied. The Wong sequences of subspaces are investigate and invoked to decompose the K^n into V* + W*, where any bases of the linear spaces V* and W* transform the matrix pencil into the Quasi-Weierstraß form. The Quasi-Weierstraß form of the matrix pencil decouples the original DAE into the underlying ODE and the pure DAE or, in other words, decouples the set of initial values into the set of consistent initial values V* and ``pure'' inconsistent initial values W* - {0}. Furthermore, V* and W* are spanned by the generalized eigenvectors at the finite and infinite eigenvalues, resp. The Quasi-Weierstraß form is used to show how chains of generalized eigenvectors at finite and infinite eigenvalues of A- E d lead to the well-known Weierstraß form. So the latter can be viewed as a generalized Jordan form. Finally, it is shown how eigenvector chains constitute a basis for the solution space of E x' = A x. |

## 2009 |

Trenn, Stephan A normal form for pure differential algebraic systems Journal Article Linear Algebra Appl., 430 (4), pp. 1070 – 1084, 2009. Abstract | Links | BibTeX | Tags: controllability, DAEs, normal-forms, observability, relative-degree @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} } 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. |