Left invertibility of hybrid dynamical systems: a framework for flying capacitor multilevel converters

In this paper, we suggest a hybrid observer consisting of a DC-DC Flying Capacitor Multilevel Converter (FCMC) with unknown discrete state. This proposed system consists of a dc-link, 4-level converter with an RL load. The state vector of the considered class of switched linear system presents unobservable modes. An observability concept known as (Z(TN)-Observability) is used to solve such problem. Following that, a hybrid observer is designed based on a coupling between a continuous and discrete observer. Indeed, this approach assumes that the available variables such as the output measurement and the estimated continuous state allow the reconstruction of the unknown discrete state which permits to detect a delay time or a produced default in these states. Finally, to validate this method some simulation results are given in order to show the effectiveness of the proposed system.