Miscellaneous

@misc{ChenTren20m,

title = {On geometric and differentiation index of nonlinear differential algebraic equations},

author = {Yahao Chen and Stephan Trenn},

editor = {Raffaella Carloni and Bayu Jayawardhana and Erjen Lefeber},

url = {https://www.beneluxmeeting.nl/2020/uploads/papers/boa.pdf, Book of Abstracts

https://stephantrenn.net/wp-content/uploads/2021/03/ChenTren20.pdf, Extended Abstract},

year  = {2020},

date = {2020-03-12},

howpublished = {Book of Abstracts - 39th Benelux Meeting on Systems and Control},

keywords = {},

pubstate = {published},

tppubtype = {misc}

}

@misc{HossTren20m,

title = {Model reduction of switched systems in time-varying approach},

author = {Sumon Hossain and Stephan Trenn},

editor = {Raffaella Carloni and Bayu Jayawardhana and Erjen Lefeber},

url = {https://www.beneluxmeeting.nl/2020/uploads/papers/boa.pdf, Book of Abstracts

https://stephantrenn.net/wp-content/uploads/2021/03/HossTren20.pdf, Extended Abstract},

year  = {2020},

date = {2020-03-12},

howpublished = {Book of Abstracts - 39th Benelux Meeting on Systems and Control},

keywords = {},

pubstate = {published},

tppubtype = {misc}

}

@misc{HuTren20m,

title = {Sliding mode observer based hysteresis compensation control for piezoelectric stacks},

author = {Jiaming Hu and Stephan Trenn},

editor = {Raffaella Carloni and Bayu Jayawardhana and Erjen Lefeber},

url = {https://www.beneluxmeeting.nl/2020/uploads/papers/boa.pdf, Book of Abstracts

https://stephantrenn.net/wp-content/uploads/2021/03/HuTren20.pdf, Extended Abstract},

year  = {2020},

date = {2020-03-12},

howpublished = {Book of Abstracts - 39th Benelux Meeting on Systems and Control},

keywords = {},

pubstate = {published},

tppubtype = {misc}

}

@misc{WijnTren20m,

title = {A forward approach to controllability of switched DAEs},

author = {Paul Wijnbergen and Stephan Trenn},

editor = {Raffaella Carloni and Bayu Jayawardhana and Erjen Lefeber},

url = {https://www.beneluxmeeting.nl/2020/uploads/papers/boa.pdf, Book of Abstracts

https://stephantrenn.net/wp-content/uploads/2021/03/WijnTren20.pdf, Extended Abstract},

year  = {2020},

date = {2020-03-12},

howpublished = {Book of Abstracts - 39th Benelux Meeting on Systems and Control},

keywords = {},

pubstate = {published},

tppubtype = {misc}

}

@misc{IervTren20m,

title = {Discontinuous Lyapunov functions for discontinous piecewise-affine systems},

author = {Raffaele Iervolino and Francesco Vasca and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2020/01/Preprint-ITV200122.pdf, Extended Abstract},

year  = {2020},

date = {2020-01-22},

abstract = {Asymptotic stability of continuous-time piecewise affine systems defined over a polyhedral partition of the state space, with possible discontinuous vector field on the boundaries, is considered. We first introduce the feasible Filippov solution concept by characterizing single-mode Caratheodory, sliding mode and forward Zeno behaviors. Then, a global  asymptotic stability result through a (possibly discontinuous) piecewise Lyapunov function is presented. The sufficient conditions are based on pointwise classifications of the trajectories which allow the identification  of crossing, unreachable and Caratheodory boundaries. It is highlighted that the sign and jump conditions of the stability theorem can be expressed in terms of linear matrix inequalities by particularizing to  piecewise quadratic Lyapunov functions and using the cone-copositivity approach. },

howpublished = {Extended Abstract},

note = {accepted for cancelled MTNS 20/21},

keywords = {},

pubstate = {published},

tppubtype = {misc}

}

@misc{Tren20m,

title = {The Laplace transform and inconsistent initial values},

author = {Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2020/01/Preprint-Tre200122.pdf, Extended Abstract},

year  = {2020},

date = {2020-01-22},

abstract = {Switches in electrical circuits may lead to Dirac impulses in the solution; a real word example utilizing this effect is the spark plug. Treating these Dirac impulses in a mathematically rigorous way is surprisingly challenging. This is in particular true for arguments made in the frequency domain in connection with the Laplace transform. A survey will be given on how inconsistent initials values have been treated in the past and how these approaches can be justified in view of the now available solution theory based on piecewise-smooth distributions.},

howpublished = {Extended Abstract},

note = {accepted for cancelled MTNS 20/21},

keywords = {},

pubstate = {published},

tppubtype = {misc}

}

@misc{LibeTren10m,

title = {The Bang-Bang Funnel Controller (long version)},

author = {Daniel Liberzon and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2017/09/Preprint-LT100806longVersion.pdf, Long version of corresponding CDC-paper},

year  = {2010},

date = {2010-08-06},

abstract = {A bang-bang controller is proposed which is able to ensure reference signal tracking with prespecified time-varying error bounds (the funnel) for nonlinear systems with relative degree one or two. For the design of the controller only the knowledge of the relative degree is needed. The controller is guaranteed to work when certain feasibility assumptions are fulfilled, which are explicitly given in the main results. Linear systems with relative degree one or two are feasible if the system is minimum phase and the control values are large enough.},

howpublished = {Extended Conference Manuscript},

note = {long version of corresponding CDC paper},

keywords = {},

pubstate = {published},

tppubtype = {misc}

}

@misc{Tren09m,

title = {Impulse free solutions for switched differential algebraic equations},

author = {Stephan Trenn},

url = {https://www.tu-ilmenau.de/fileadmin/media/math/Preprints/2009/09_03_trenn.pdf, TU-Ilmenau Preprint Server

https://stephantrenn.net/wp-content/uploads/2021/03/Preprint-Tre090123.pdf, Preprint},

year  = {2009},

date = {2009-01-23},

abstract = {Linear switched differential algebraic equations (switched DAEs) are studied. First, a suitable solution space is introduced, the space of so called piecewise-smooth distributions. Secondly, sufficient conditions are given which ensure that all solutions of the switched DAE are impulse and/or jump free. These conditions are easy to check and are expressed directly in the systems original data. As an example a simple electrical circuit with a switch is analyzed.},

howpublished = {Preprint},

note = {After the initial submission, I decided not to revise this manuscript and instead included most of the content in the paper "Switched nonlinear differential algebraic equations: Solution theory, Lyapunov functions, and stability" (joint work with Daniel Liberzon), which appeared 2012 in Automatica.},

keywords = {},

pubstate = {published},

tppubtype = {misc}

}