Wellposedness and stabilization of a class of infinite dimensional bilinear control systems

We consider a class of infinite dimensional systems involving a control function u taking values in [0; 1]. This class contains, in particular, the average models of some infinite dimensional switched systems. We prove that the system is wellposed and obtain some regularity properties. Moreover, when u is given in an appropriate feedback form and the system satisfies appropriate observability assumptions, we show that the system is weakly stable. The main example concerns the analysis and stabilization of a model of Boost converter connected to a load via a transmission line. The main novelty consists in the fact that we give a rigorous wellposedness and stability analysis of coupled systems, in the presence of duty cycles.