GT Shy

Séminaire le 10 Novembre 2015, 09h30 à ENSTA ParisTech (salle TBA)
C. Briat and A. Girard

Programme :
- 9h30-10h00 Accueil (café)
- 10h00 - 11h00 Corentin Briat (ETH Zürich) : Convex conditions for stability analysis and stabilization of linear aperiodic impulsive systems with applications to asynchronous sampled-data systems
This talk is about the analysis and control of linear impulsive systems using clock-dependent Lyapunov functions. Necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas. Extensions to the stability of aperiodic systems under minimum, maximum and ranged dwell-times are then derived. These stability criteria are, in turn, losslessly extended to stabilization using a particular, yet broad enough, class of state-feedback controllers, providing then a convex solution to the (previously open) problem of dwell-time stabilization of impulsive systems using hybrid stability criteria. By finally relying on the representability of sampled-data systems as impulsive systems, the problem of robust stabilization of periodic and aperiodic uncertain sampled-data systems is straightforwardly solved using the same ideas. Several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach.

- 11h00 - 12h00 Antoine Girard (CNRS, L2S): Reachability analysis of linear hybrid systems - application to stability analysis of linear aperiodic impulsive systems.
In the first part of this talk, I will present the basics of computational reachability analysis for hybrid systems. I will then focus on the presentation of scalable and accurate algorithms for reachability analysis of linear systems. In the second part of the talk, I will show how these algorithms can serve for stability analysis of a class of linear aperiodic impulsive systems. Applications of our approach to verification and synthesis of timing contracts for implementation of embedded controllers will conclude the talk.

Les organisateurs C. Bonnet, A. Chapoutot, P. Mason