Fixed Poles for Non Minimal Systems: a Geometric Approach

When considering the set of solutions, e.g. by state or measurement feedback, of a given control problem (e.g. disturbance decoupling), complete pole placement is usually not possible, due to the so-called fixed poles: these are dynamics of the compensated system, occuring in any solution (within the chosen class). These fixed poles have two origins: some are present, for any considered control problem, because of possible non minimality of the state description (in the Kalman sense, i.e. controllability and observability). The other are due to the particular control problem which the feedback law solves. We show here how non minimality impacts the corresponding geometric solvability conditions and how the global set of the fixed poles of such control problems can be characterised in the general case (i.e. without any controllability or observability assumption). Copyright © 2005 IFAC