On order overspecification for a direct adaptive pole placer

Indirect adaptive pole placers combining plant parameter estimation and algebraic solution of the pole placement problem require, at least, a minimal convergent plant parameterization to avoid requesting infinite controller gains. This is impossible if the plant order is overspecified. A new direct adaptive pole placer, based on the inclusion by Elliott of the Bezout identity in the prediction error, is shown in this paper to, at least sometimes, bypass this restriction.