My name is Stephan Trenn and I am researcher in the area of applied mathematics, for more informations see the About Me page. You may also want to browse my publications, which can be filtered e.g. by keywords and coauthors. I also have profiles at Google Scholar, ResearchGate and ORCID.
Below, I will regularly post news related to my research.
Finally, my Erdös number (see also here) is 4.
(Eugene P. Ryan – Geoffrey R. Burton – George B. Purdy – Paul Erdös)
We have submitted the manuscript
Stability analysis for switched discrete-time linear singular systems Unpublished
2019, (submitted for publication).
My three Vietnames co-authors and I have analyzed the stability of switched linear singular system in discrete-time. The results build on our recently introduced notion of a one-step-map for index-1 switched singular systems:
We have submitted the following four papers to the CDC 2019 in Nice, France.
Finally, we have finished our paper
and submitted it for publication.
We have started to work on this topic almost four years ago when I visited Benevento. Inspired by the promising approach of using the cone-copositivity approach to find Lyapunov functions for piecewise-affine (PWA) systems in an automatic way, we were trying to extend this idea in two main directions: 1) We wanted to allow for discontinuous Lyapunov functions and 2) we wanted to cover also sliding and Zeno solutions. We obtained first results by focusing on the first point (i.e. we only considered classical solutions) and presented these ideas at the CDC 2017 in Melbourne, Australia. It turned out that the technicalities involved in dealing with general Filippov solutions were quite tricky and we still haven’t resolved all of them. In particular, we had to make two technical assumptions for PWA systems which we believe are always satisfied, because we could not construct counter examples which violates these assumptions, but we were also not able to prove them so far. Furthermore, classifying boundaries as crossing, non-reachable and sliding turned out to be harder as expected as well, in particular, due to the presence of Zeno-behavior. Nevertheless we have a very strong (i.e. not very conservative) Lyapunov stability theorem which is formulated in terms of pointwise-conditions. In order to use the cone-copositive approach it is necessary to make some uniformity assumption on the solution behavior along the boundaries, but these assumptions do not exclude Zeno and sliding behavior and allows discontinuities of the Lyapunov function on crossing boundaries.
We are now looking forward to receive constructive feedback from our peers to further improve on the manuscript for the final published version.
The slides of my talk “Asymptotic Tracking with Funnel Control” given at the 90th GAMM Annual Meeting in Vienna, Austria, are available on the Talks page.
was recently accepted for publications in Automatica, as soon as I have the final bibliographical data I will update the corresponding entry in my publication list.
The slides of my talk “Zeno-like behavior in coupled systems of switched DAEs and PDEs” which was presented at Annual Meeting of the SPP 1962 are now available on my Talks page.
is accepted for publication in Automatica as a regular paper. Once the exact publication details are available, I will update the information on my Publication page and will also add a doi-link.
The slides of my talk “Switch induced instabilities for stable power system DAE models” held at the IFAC Conference on Analysis and Design of Hybrid Systems (ADHS2018), Oxford, UK are available on my Talks page.
The slides of my talk “Switched differential algebraic equations: Jumps and impulses” are available on my Talks page. Thanks to Markus Mueller and Tim Hughes for their kind hospitality.
The slides of my talk “Optimal Control of switched DAEs” are available on my Talks page. Thanks to Karl Worthmann who invited me to contribute to the session on “Model based control: analysis and modelling”.