October 2020

16 octobre 2020 – 10h, salle Europe

Speaker: Matteo Della Rossa
Title: Graph-theory-based Lyapunov functions for switching systems
Abstract: We use a graph-theory-based argument to propose a novel Lyapunov construction for continuous-time switching systems. Starting with a finite family of continuously differentiable functions, the inequalities involving these functions and the vector fields of the switching system are encoded in a direct and labeled graph. Relying on the (path-)completeness of this graph,  we introduce a signal-dependent Lyapunov function, providing sufficient conditions for stability under fixed-time or dwell-time switching hypothesis. For the case of linear systems, our conditions turn into linear matrix inequalities (LMI), and thus they are compared with previous results, via numerical examples.
Slides

Speaker: Quentin Vila
Title: 7 amazing facts about Borel measures that you (almost surely) didn’t know
Abstract: Noone remembers today the picture of Henri Lebesgue, in 1901, singing joyfully in the teacher’s lounge at the central high school of Nancy at the moment when he first introduced the notion of measure: « Les mesures sont nos amies, il faut les aimer aussi ». This is probably because he might have never really said those words. He would have been pretty right though; this is the reason why I propose to you, my dear MAC team, a carefully planned overview of colorful facts about measures. The presentation will start with an example, then our trip will take us through probabilities, measures, limit processes, measurable sets, Bochner integrals, distributions, limit scales, the Lasserre hierarchy and the Devil’s staircase. If I dare, I will even draw it to a close with another little song.
Slides