Determination of generic dimensions of controllable subspaces and its application

The controllable subspace and its dimension of a structured linear system vary as a function of the free parameters. However, the dimension is stable in the sense that it takes, for almost any system parameters, some maximal constant which is the generic rank of the controllability matrix. In this paper, this maximal constant is called the generic dimension of the controllable subspace. Two simple methods for determining generic dimensions of controllable subspaces are derived. As an application, the results are applied to the determination of system types of linear multivariable unity feedback systems.