On controllability and full-actuation of the descriptor linear system

Complete controllability and full-actuation of descriptor linear system (DLS) with single input is investigated in this article. Using the standard decomposition, the DLS is decomposed into a slow subsystem and a fast subsystem. A novel canonical form is proposed for the completely controllable fast subsystem, based on which, the fast subsystem is equivalently transformed into a simplest fully-actuated system. The canonical form of the completely controllable DLS is derived. Using the proposed canonical form, the relation between the controllability and full-actuation of the DLS is established. Three examples are presented to demonstrate the effectiveness of the proposed results.