Determination of the Dimensions of Strong Structural Controllable Subspaces

In this paper the notion dimension of strong structural controllable subspaces of structured linear systems is introduced and a method for the determination is given. This proposed dimension is a lower bound for the dimensions of the controllable subspaces of all parameterized systems with the same structure. For this purpose the existing concepts of structural and strong structural controllability are revised and an algebraic characterization of the dimension of the strong structural controllable subspace is given. Furthermore, a new structured–based upper bound for the number of uncontrollable eigenvalues at zero is presented. Finally, the proposed algebraic criteria are applied to the controllability analysis of a linear drivetrain model of a parallel hybrid electric vehicle.