On the Construction of Jordan Chains in the Eigenstructure Assignment for Output-Nulling Subspaces

This paper investigates several aspects related with the eigenstructure assignment problem for output-nulling subspaces. In particular, we deliver an alternative method for the computation of the feedback matrix that renders these subspaces invariant with respect to the closed-loop system matrix and assigns a defective eigenstructure in the closed-loop eigenstructure restricted to these subspaces. We show that this method, which consists in building the Jordan chains starting from the generalized eigenspace to the null-space of the Rosenbrock matrix, provides additional freedom in the resulting basis matrix.