Adaptive IIR filtering: convergence speed properties in the undermodelled case

Previous results based on balanced realization theory and concerning the local convergence speed of adaptive IIR filters apply to the sufficient order case. In the undermodelled case, situations of greater practical interest are those in which the order chosen for the adaptive filter provides a good approximation of the system being modelled. A relevant question is then if the existence of a good approximation of the system implies a good approximation of the sufficient order convergence speed properties. We address this problem here, based on the same balanced realization theory framework. Our results suggest a positive answer to the question.