Asymptotic properties of set membership identification algorithms

This paper addresses the asymptotic worst-case properties of set membership identification (SMID) algorithms. We first present a set membership identification algorithm which can be used with a model structure consisting of parametric and nonparametric uncertainty, as well as output additive disturbances. This algorithm is then studied in the context of asymptotic worst-case behavior. We derive lower bounds on the worst-case achievable identification error measured by the volume, as well as the sum-of-sidelengths of the identified ellipsoidal uncertainty sets. We then show that there exist inputs which can shrink the uncertainty sets to these lower bounds.