Geometric characterizations of the fixed poles for some control problems

The aim of the paper is to present some geometric characterizations for the fixed poles of some control problems and to enhance a major property of some particular invariant subspaces (self-bounded controlled invariants and self-hidden conditioned invariants) associated with the disturbance rejection by state or dynamic measurement feedback, the decoupling problem by (regular) state feedback and the simultaneous decoupling and disturbance rejection problem by (regular) state feedback. Such particular invariant subspaces are indeed the geometric supports for the construction of optimal solutions in the sense of maximal pole placement abilities