14h00-15h00 – Salle du conseil (L2S)
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:
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.
Biography. 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.