Observability of Switched Linear Systems Based Geometrical Conditions: an Application to DC/DC Multilevel Converters

Switching systems are systems comprising a set of continuous dynamics orchestrated by a switching signal. This type of system can represent a very broad spectrum of systems such as: power electronics, multi-controller systems, robotics, electromechanical systems and systems with discontinuities. As a result, the development of tools allowing analyze the dynamic properties such as observability is essential before any order design step. In this paper,a necessary and sufficient condition for the continuous state observability for a given periodic sequence of discrete modes is elaborated for switched linear system. The characterization of the continuous state observability is derived using geometrical tools. Concrete example as multilevel converter i.e two-cells is reported to highlight the derived results. Super twisting sliding mode observer are developed. This one is applied to the estimation of the floating capacitor voltage of the converter based on the load current measurement and the knowledge of the periodic sequence of discrete modes. Simulation results confirm the analytical demonstrations and prove the effectiveness of observer.