ASYMPTOTIC PROPERTIES OF SET MEMBERSHIP IDENTIFICATION ALGORITHMS

This paper addresses the asymptotic worst-case properties of set membe rship identification (SMID) algorithms. We first present a set members hip identification algorithm which can be used with a model structure consisting of parametric and nonparametric uncertainty, as well as out put additive disturbances. This algorithm is then studied in the conte xt of asymptotic worst-case behavior. We derive lower bounds on the wo rst-case achievable identification error measured by the volume, as we ll as the sum-of-sidelengths of the identified ellipsoidal uncertainty sets. We then show that there exist inputs which can shrink the uncer tainty sets to these lower bounds.