On generalized controllability canonical form with multiple input variables

Abstract

This paper proposes a generalized controllability canonical form for linear multi-input systems by extending the normal controllability canonical forms. It is shown that there exists appropriate similarity transformation for any non-trivial system to transform it into a generalized controllability canonical form, even if the system is not completely controllable. The potential application scenarios are reviewed, especially for large-scale networked systems. The Luenberger format is taken as an instance to delineate the configuration of a generalized form. A numerical example is presented to demonstrate the relevant algorithm.