Stability and controllability analysis of infinite-dimensional singularly perturbed systemsMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

This talk is devoted to infinite-dimensional singularly perturbed systems, namely, partial differential equations. To be more precise, such systems admit two different time-scales, i.e. one can see them as the coupling between a fast system and a slow system. This may lead to several technical issues - for example, in numerical analysis, where the time steps have to be adapted according to the ratio between the time scales. Another way is to compute approximated and decoupled systems, called the reduced order and the boundary layer systems, for which the analysis is easier. This talk focuses on control theory. In particular, the singular perturbation allows, at least in finite dimension, to deduce the stability of the full-system thanks to the stability analysis of the approximated systems (if the fast system is sufficiently fast). In infinite-dimension, this analysis might be not possible, and this talk proposes some counter-examples together with examples for which such property holds. It is a joint work with Gonzalo Arias, Eduardo Cerpa and Guilherme Mazanti.