A reduced order framework applied to linear systems with constrained controls

A generic reduced order framework to deal with some constrained control problems in linear systems is presented. The class of regulation schemes considered uses full state feedback to make positively invariant with respect to (w.r.t.) the closed loop system, a polyhedron construct from the state feedback matrix. In this case, using partial eigenstructure assignment techniques, it is possible to solve some constrained control problems using a reduced order system obtained by the projection of the trajectory of the original system in a subspace associated with the undesirable open-loop eigenvalues.