Geometric structure and properties of LTI systems in the controller canonical form

In this paper we analyse the geometric properties of systems in the controller canonical form. We show that using a technique based on the calculation of null-spaces of the Rosenbrock system matrix pencil facilitates the computation of the fundamental geometric subspaces for such systems. It is also shown how this geometric analysis can be exploited to derive necessary and sufficient conditions for the solution of the global monotonic tracking control problem solely in terms of the problem data.