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.

## 2017 |

Mostacciuolo, Elisa; Trenn, Stephan; Vasca, Francesco Averaging for switched DAEs: convergence, partial averaging and stability Journal Article Automatica, 82 , pp. 145–157, 2017. Abstract | Links | BibTeX | Tags: averaging, DAEs, stability, switched-DAEs, switched-systems @article{MostTren17, title = {Averaging for switched DAEs: convergence, partial averaging and stability}, author = {Elisa Mostacciuolo and Stephan Trenn and Francesco Vasca}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-MTV170407.pdf, Preprint}, doi = {10.1016/j.automatica.2017.04.036}, year = {2017}, date = {2017-08-01}, journal = {Automatica}, volume = {82}, pages = {145--157}, abstract = {Averaging is a useful technique to simplify the analysis of switched systems. In this paper we present averaging results for the class of systems described by switched differential algebraic equations (DAEs). Conditions on the consistency projectors are given which guarantee convergence towards a non-switched averaged system. A consequence of this result is the possibility to stabilize switched DAEs via fast switching. We also study partial averaging in case the consistency projectors do not satisfy the conditions for convergence; the averaged system is then still a switched system, but is simpler than the original. The practical interest of the theoretical averaging results is demonstrated through the analysis of the dynamics of a switched electrical circuit.}, keywords = {averaging, DAEs, stability, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {article} } Averaging is a useful technique to simplify the analysis of switched systems. In this paper we present averaging results for the class of systems described by switched differential algebraic equations (DAEs). Conditions on the consistency projectors are given which guarantee convergence towards a non-switched averaged system. A consequence of this result is the possibility to stabilize switched DAEs via fast switching. We also study partial averaging in case the consistency projectors do not satisfy the conditions for convergence; the averaged system is then still a switched system, but is simpler than the original. The practical interest of the theoretical averaging results is demonstrated through the analysis of the dynamics of a switched electrical circuit. |

## 2016 |

Trenn, Stephan Stabilization of switched DAEs via fast switching Inproceedings PAMM - Proc. Appl. Math. Mech., pp. 827–828, WILEY-VCH Verlag, 2016, ISSN: 1617-7061. Abstract | Links | BibTeX | Tags: averaging, DAEs, stability, switched-DAEs, switched-systems @inproceedings{Tren16, title = {Stabilization of switched DAEs via fast switching}, author = {Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-Tre160511.pdf, Preprint}, doi = {10.1002/pamm.201610402}, issn = {1617-7061}, year = {2016}, date = {2016-05-12}, booktitle = {PAMM - Proc. Appl. Math. Mech.}, volume = {16}, number = {1}, pages = {827--828}, publisher = {WILEY-VCH Verlag}, abstract = {Switched differential algebraic equations (switched DAEs) can model dynamical systems with state constraints together with sudden structural changes (switches). These switches may lead to induced jumps and can destabilize the system even in the case that each mode is stable. However, the opposite effect is also possible; in particular, the question of finding a stabilizing switching signal is of interest. Two approaches are presented how to stabilize a switched DAE via fast switching.}, keywords = {averaging, DAEs, stability, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } Switched differential algebraic equations (switched DAEs) can model dynamical systems with state constraints together with sudden structural changes (switches). These switches may lead to induced jumps and can destabilize the system even in the case that each mode is stable. However, the opposite effect is also possible; in particular, the question of finding a stabilizing switching signal is of interest. Two approaches are presented how to stabilize a switched DAE via fast switching. |

## 2015 |

Trenn, Stephan Distributional averaging of switched DAEs with two modes Inproceedings Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan, pp. 3616–3620, 2015. Abstract | Links | BibTeX | Tags: averaging, CDC, DAEs, piecewise-smooth-distributions, switched-DAEs, switched-systems @inproceedings{Tren15, title = {Distributional averaging of switched DAEs with two modes}, author = {Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-Tre150812.pdf, Preprint}, doi = {10.1109/CDC.2015.7402779}, year = {2015}, date = {2015-12-04}, booktitle = {Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan}, pages = {3616--3620}, abstract = {The averaging technique is a powerful tool for the analysis and control of switched systems. Recently, classical averaging results were generalized to the class of switched differential algebraic equations (switched DAEs). These results did not consider the possible Dirac impulses in the solutions of switched DAEs and it was believed that the presence of Dirac impulses does not prevent convergence towards an average model and can therefore be neglected. It turns out that the first claim (convergence) is indeed true, but nevertheless the Dirac impulses cannot be neglected, they play an important role for the resulting limit. This note first shows with a simple example how the presence of Dirac impulses effects the convergence towards an averaged model and then a formal proof of convergence in the distributional sense for switched DAEs with two modes is given.}, keywords = {averaging, CDC, DAEs, piecewise-smooth-distributions, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } The averaging technique is a powerful tool for the analysis and control of switched systems. Recently, classical averaging results were generalized to the class of switched differential algebraic equations (switched DAEs). These results did not consider the possible Dirac impulses in the solutions of switched DAEs and it was believed that the presence of Dirac impulses does not prevent convergence towards an average model and can therefore be neglected. It turns out that the first claim (convergence) is indeed true, but nevertheless the Dirac impulses cannot be neglected, they play an important role for the resulting limit. This note first shows with a simple example how the presence of Dirac impulses effects the convergence towards an averaged model and then a formal proof of convergence in the distributional sense for switched DAEs with two modes is given. |

Mostacciuolo, Elisa; Trenn, Stephan; Vasca, Francesco Averaging for non-homogeneous switched DAEs Inproceedings Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan, pp. 2951–2956, 2015. Abstract | Links | BibTeX | Tags: application, averaging, CDC, DAEs, switched-DAEs, switched-systems @inproceedings{MostTren15b, title = {Averaging for non-homogeneous switched DAEs}, author = {Elisa Mostacciuolo and Stephan Trenn and Francesco Vasca}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-MTV150901.pdf, Preprint}, doi = {10.1109/CDC.2015.7402665}, year = {2015}, date = {2015-12-02}, booktitle = {Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan}, pages = {2951--2956}, abstract = {Averaging is widely used for approximating the dynamics of switched systems. The validity of an averaged model typically depends on the switching frequency and on some technicalities regarding the switched system structure. For homogeneous linear switched differential algebraic equations it is known that an averaged model can be obtained. In this paper an averaging result for non-homogeneous switched systems is presented. A switched electrical circuit illustrates the practical interest of the result.}, keywords = {application, averaging, CDC, DAEs, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } Averaging is widely used for approximating the dynamics of switched systems. The validity of an averaged model typically depends on the switching frequency and on some technicalities regarding the switched system structure. For homogeneous linear switched differential algebraic equations it is known that an averaged model can be obtained. In this paper an averaging result for non-homogeneous switched systems is presented. A switched electrical circuit illustrates the practical interest of the result. |

Mostacciuolo, Elisa; Trenn, Stephan; Vasca, Francesco Partial averaging for switched DAEs with two modes Inproceedings Proc. 2015 European Control Conf. (ECC), Linz, Austria, pp. 2896–2901, 2015. Abstract | Links | BibTeX | Tags: averaging, DAEs, switched-DAEs, switched-systems @inproceedings{MostTren15a, title = {Partial averaging for switched DAEs with two modes}, author = {Elisa Mostacciuolo and Stephan Trenn and Francesco Vasca}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-MTV150316.pdf, Preprint}, doi = {10.1109/ECC.2015.7330977}, year = {2015}, date = {2015-03-01}, booktitle = {Proc. 2015 European Control Conf. (ECC), Linz, Austria}, pages = {2896--2901}, abstract = {In this paper an averaging result for switched systems whose modes are represented by means of differential algebraic equations (DAEs) is presented. Homogeneous switched DAEs with periodic switchings between two modes are considered. It is proved that a (switched) averaged system can be defined also in the presence of state jumps whose amplitude does not decrease with the increasing of the switching frequency. A switched capacitor electrical circuit is considered as an illustrative example.}, keywords = {averaging, DAEs, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } In this paper an averaging result for switched systems whose modes are represented by means of differential algebraic equations (DAEs) is presented. Homogeneous switched DAEs with periodic switchings between two modes are considered. It is proved that a (switched) averaged system can be defined also in the presence of state jumps whose amplitude does not decrease with the increasing of the switching frequency. A switched capacitor electrical circuit is considered as an illustrative example. |

## 2013 |

Iannelli, Luigi; Pedicini, Carmen; Trenn, Stephan; Vasca, Francesco An averaging result for switched DAEs with multiple modes Inproceedings Proc. 52nd IEEE Conf. Decis. Control, Florence, Italy, pp. 1378 - 1383, 2013. Abstract | Links | BibTeX | Tags: averaging, CDC, DAEs, switched-DAEs, switched-systems @inproceedings{IannPedi13b, title = {An averaging result for switched DAEs with multiple modes}, author = {Luigi Iannelli and Carmen Pedicini and Stephan Trenn and Francesco Vasca}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-IPTV130911.pdf, Preprint}, doi = {10.1109/CDC.2013.6760075}, year = {2013}, date = {2013-12-10}, booktitle = {Proc. 52nd IEEE Conf. Decis. Control, Florence, Italy}, pages = {1378 - 1383}, abstract = {The major motivation of the averaging technique for switched systems is the construction of a smooth average system whose state trajectory approximates in some sense the state trajectory of the switched system. Averaging of dynamic systems represented by switched ordinary differential equations (ODEs) has been widely analyzed in the literature. The averaging approach can be useful also for the analysis of switched differential algebraic equations (DAEs). Indeed by analyzing the evolution of the switched DAEs state it is possible to conjecture the existence of an average model. However a trivial generalization of the ODE case is not possible due to the presence of state jumps. In this paper we discuss the averaging approach for switched DAEs and an approximation result is derived for homogenous switched linear DAE with periodic switching signals commuting among several modes. This approximation result extends a recent averaging result for switched DAEs with only two modes. Numerical simulations confirm the validity of the averaging approach for switched DAEs.}, keywords = {averaging, CDC, DAEs, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } The major motivation of the averaging technique for switched systems is the construction of a smooth average system whose state trajectory approximates in some sense the state trajectory of the switched system. Averaging of dynamic systems represented by switched ordinary differential equations (ODEs) has been widely analyzed in the literature. The averaging approach can be useful also for the analysis of switched differential algebraic equations (DAEs). Indeed by analyzing the evolution of the switched DAEs state it is possible to conjecture the existence of an average model. However a trivial generalization of the ODE case is not possible due to the presence of state jumps. In this paper we discuss the averaging approach for switched DAEs and an approximation result is derived for homogenous switched linear DAE with periodic switching signals commuting among several modes. This approximation result extends a recent averaging result for switched DAEs with only two modes. Numerical simulations confirm the validity of the averaging approach for switched DAEs. |

Iannelli, Luigi; Pedicini, Carmen; Trenn, Stephan; Vasca, Francesco Averaging for switched DAEs Inproceedings PAMM - Proc. Appl. Math. Mech., pp. 489–490, WILEY-VCH Verlag, 2013, ISSN: 1617-7061. Abstract | Links | BibTeX | Tags: averaging, DAEs, switched-DAEs, switched-systems @inproceedings{IannPedi13c, title = {Averaging for switched DAEs}, author = {Luigi Iannelli and Carmen Pedicini and Stephan Trenn and Francesco Vasca}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-IPTV130527.pdf, Preprint}, doi = {10.1002/pamm.201310237}, issn = {1617-7061}, year = {2013}, date = {2013-10-01}, booktitle = {PAMM - Proc. Appl. Math. Mech.}, volume = {13}, number = {1}, pages = {489--490}, publisher = {WILEY-VCH Verlag}, abstract = {Switched differential-algebraic equations (switched DAEs) E_sigma(t) x'(t) = A_sigma(t) x(t) are suitable for modeling many practical systems, e.g. electrical circuits. When the switching is periodic and of high frequency, the question arises whether the solutions of switched DAEs can be approximated by an average non-switching system. It is well known that for a quite general class of switched ordinary differential equations (ODEs) this is the case. For switched DAEs, due the presence of the so-called consistency projectors, it is possible that the limit of trajectories for faster and faster switching does not exist. Under certain assumptions on the consistency projectors a result concerning the averaging for switched DAEs is presented.}, keywords = {averaging, DAEs, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } Switched differential-algebraic equations (switched DAEs) E_sigma(t) x'(t) = A_sigma(t) x(t) are suitable for modeling many practical systems, e.g. electrical circuits. When the switching is periodic and of high frequency, the question arises whether the solutions of switched DAEs can be approximated by an average non-switching system. It is well known that for a quite general class of switched ordinary differential equations (ODEs) this is the case. For switched DAEs, due the presence of the so-called consistency projectors, it is possible that the limit of trajectories for faster and faster switching does not exist. Under certain assumptions on the consistency projectors a result concerning the averaging for switched DAEs is presented. |

Iannelli, Luigi; Pedicini, Carmen; Trenn, Stephan; Vasca, Francesco On averaging for switched linear differential algebraic equations Inproceedings Proc. 12th European Control Conf. (ECC) 2013, Zurich, Switzerland, pp. 2163 – 2168, 2013. Abstract | Links | BibTeX | Tags: averaging, DAEs, switched-DAEs, switched-systems @inproceedings{IannPedi13a, title = {On averaging for switched linear differential algebraic equations}, author = {Luigi Iannelli and Carmen Pedicini and Stephan Trenn and Francesco Vasca}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-IPTV130326.pdf, Preprint http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6669240, IEEE Xplore Article Number 6669240}, year = {2013}, date = {2013-07-02}, booktitle = {Proc. 12th European Control Conf. (ECC) 2013, Zurich, Switzerland}, pages = {2163 -- 2168}, abstract = {Averaging is an effective technique which allows the analysis and control design of nonsmooth switched systems through the use of corresponding simpler smooth averaged systems. Approximation results and stability analysis have been presented in the literature for dynamic systems described by switched ordinary differential equations. In this paper the averaging technique is shown to be useful also for the analysis of switched systems whose modes are represented by means of differential algebraic equations (DAEs). An approximation result is derived for a simple but representative homogenous switched DAE with periodic switching signals and two modes. Simulations based on a simple electric circuit model illustrate the theoretical result.}, keywords = {averaging, DAEs, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } Averaging is an effective technique which allows the analysis and control design of nonsmooth switched systems through the use of corresponding simpler smooth averaged systems. Approximation results and stability analysis have been presented in the literature for dynamic systems described by switched ordinary differential equations. In this paper the averaging technique is shown to be useful also for the analysis of switched systems whose modes are represented by means of differential algebraic equations (DAEs). An approximation result is derived for a simple but representative homogenous switched DAE with periodic switching signals and two modes. Simulations based on a simple electric circuit model illustrate the theoretical result. |