Flatness of interconnected linear systems and applications to electrical systems

Abstract

In this paper, we completely describe flatness of the simplest class of interconnected systems: we consider an interconnection of (controllable) single-input linear subsystems in dimension two with a star topology and a linear interconnection dynamics (with no inputs acting directly on the interconnection variable). First, we observe that even if each subsystem is flat, flatness of the global interconnected system is not necessarily preserved. Then, we give necessary and sufficient verifiable conditions for flatness of the interconnected system. When the interconnected system is flat, we analyze how its flat output depends on the interconnection variable and how it can be expressed in function of the flat outputs of each subsystem. Finally, we show how our results can be applied to electrical power systems.