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.