Fixed poles of disturbance rejection by dynamic output feedback: Geometric and structural approaches

This paper is concerned with the Disturbance Rejection by Dynamic Output Feedback problem and aims at proposing new geometric and structural characterizations for the Fixed Poles of this problem in the case of minimal (controllable and observable) systems. The key notions behind theses results are those of self-bounded and self-hidden invariant subspaces as introduced by Basile and Marro. The Fixed Poles are uniquely characterized, moreover the geometric subspaces (some particular (C, A, B)-pairs) which lead to the minimal solutions (for which all the other poles can be freely assigned) are not unique. As a corollary, we propose a structural necessary and sufficient condition for the existence of (internally) stable solutions, which generalizes the sufficient structural condition proposed by Basile and Marro.