18/06/2018 Seminar of Fabian Wirth
Date de publication : Apr 05, 2018 7:52:31 AM
Date: 18/06/2018, 14h00
Location: AMPERE, Salle M1B, Batiment St Exupery
Speaker: Fabian Wirth, Professor of university of Passau
Title : Stabilization of differential-algebraic systems by switching
Abstract : One possible way of stabilizing switched linear systems is to choose the
switching instances in such a manner that the resulting time-varying
system is exponentially stable. It is a classical result for switched
linear ordinary differential equations that this is possible if there
exists a Hurwitz matrix in the convex hull of the constituent matrices
of the switched linear system.
For switched differential algebraic equations this result cannot be
extended directly. On the one hand the switching may induce impulsive
components of solutions which destroy stability. On the other hand it is
by no means clear how the concept of convex hull can be transferred to
the differential algebraic case. In particular with the aim of
obtaining a meaningful construction from the point of view of dynamical
systems.
In the talk we will discuss several sufficient conditions which allow
the construction of stabilizing switching sequences for DAEs. One
approach relies on the approximation of the DAE dynamics by systems of
ordinary differential equations with fast dynamics, i.e. singularly
perturbed systems. Another method uses estimates for the discontinuities
induced by switching to obtain stabilizing switching sequences.
The talk is based on joint work with Andrii Mironchenko and Kai Wulff.