Abstract: In this talk, we will present some recently obtained approximate and exact controllability conditions in L^p spaces for a class of linear one-dimensional hyperbolic systems, which are expressed under the form of Hautus-type conditions. We first reformulate the controllability problem in an equivalent way in terms of the control of linear difference equations. Then, instead of following the standard approach in the control of PDEs based on proving an observability inequality, we make use of realization theory in order to express controllability properties in terms of solving (exactly or approximately) a Bézout identity over a suitable functional space, which can in turn be related to Hautus-type conditions. We finally apply our controllability results to a problem of flow on networks. This talk is based on a joint work with Yacine Chitour, Sébastien Fueyo, and Mario Sigalotti.
