# Dwell-time stability analysis for switched systems: from linear to (very structured) non-linear subsystems.

Date : 26/01/2023 De 16h00 A 17h00

https://mines-paristech.zoom.us/j/93863554850?pwd=dkFjTWZlSUV6bkdOQjR3L25FUXFvZz09
ID de la réunion / Meeting ID : 93863554850
Mot de passe / Password : 613093

SPEAKER
Matteo Della Rossa, UCLouvain (Louvain-La-Neuve, Belgium)

TITLE
Dwell-time stability analysis for switched systems: from linear to (very structured) non-linear subsystems.

ABSTRACT
Since the 90s it is known that, starting from a finite family of asymptotically stable linear subsystems, two important facts hold:
- The arising switched system is not, in general, asymptotically stable, if it is free to commute/switch with unbounded/unconstrained frequency.
- On the other hand, there always exists a large enough waiting-time, also called dwell-time, for which the arising (constrained) switched system is still'' asymptotically stable.
It is also known that this second statement is false, in whole generality, for finite families of non-linear subsystems.
In this talk, I present some recent results which partially extend/adapt the dwell-time stability analysis for two of the "simplest'" non-linear dynamics one can think about: affine and homogeneous subsystems.
In the case of affine subsystems, due to the presence of multiple equilibria, more general notions of stability/boundedness are introduced and studied, highlighting the relations with the stability of the linear part of the system under the same class of dwell-time switching signals.
In the case of homogeneous subsystems, we investigate different scenarios where all the subsystems have a common asymptotically stable equilibrium, but for the switched system, the equilibrium is not uniformly GAS for
arbitrarily large values of dwell-time. Anyhow, thanks to the homogeneity property, we provide local/practical stability results.

BIO

Matteo Della Rossa obtained a master degree in Mathematics (cum laude) from University of Udine (Italy), in 2017. He graduated from University of Toulouse at LAAS-CNRS (Toulouse, France) in 2020 where he obtained the Ph.D. degree in automatic control. From November 2020, he holds a postdoctoral position at UCLouvain (Louvain-La-Neuve, Belgium). His main research interests include nonlinear control, switched and hybrid dynamical systems, nonsmooth analysis and nonsmooth Lyapunov functions.