Speaker Prof. Stephan Trenn
Science and Engineering, University of Groningen, Netherlands
Date｜Time Mar 5 (Thursday), 2026｜17:00
Zoom https://snu-ac-kr.zoom.us/my/jingyu.lee
Abstract
We are interested in the relationship between the stability properties of a singularly perturbed switched system and those of the corresponding limiting switched system. In some recent work, it has been shown that for a large class of singularly perturbed systems the worst case exponential growth rate for sufficiently small perturbation parameters is lower bounded by the growth rate of the limiting switched system. However, examples show that there could be a positive gap between these bounds. Here we want to investigate this gap further by first observing that the limiting switching system is in fact a switched differential-algebraic equation (switched DAE) for which numerous stability results are already available. Based on the underlying geometric structure of the switched DAE we introduce the concept of structurally aligned singular perturbations and show for the commuting case that indeed there is no gap. We also provide an example which has a commuting limiting switched DAE, but for which the singular perturbations are not structurally aligned and there is indeed a gap between the growth bounds.
Biography
Stephan Trenn received his Ph.D. (Dr. rer. nat.) within the field of differential algebraic systems and distribution theory at the Ilmenau University of Technology, Germany, in 2009. Afterwards, he held Postdoc positions at the University of Illinois at Urbana-Champaign, USA (2009–2010) and at the University of Würzburg, Germany(2010–2011). After being an Assistant Professor (Juniorprofessor) at the University of Kaiserslautern, Germany, he became Associate Professor for Systems and Control at the University of Groningen, Netherlands, in 2017. He is an Associate Editor for the journals Systems and Control Letters, Nonlinear Analysis: Hybrid Systems, IEEE Control Systems Letters, and DAE Panel.
