Connection of multiplicative/relative perturbation in coprime factors and gap metric uncertainty

In this paper, it is shown that a linear uncertain system described by a certain L-infinity multiplicative or relative perturbation in its coprime factors that are not necessarily normalized, is the same as the one described by a gap or upsilon-gap metric ball. Hence all the stability robustness results for gap or upsilon-gap metric uncertainty carry over to this type of coprime factor perturbation. Uncertain systems described by H-infinity multiplicative or relative perturbations in coprime Factors are also studied in this paper. Necessary and sufficient conditions for robust stability of a feedback system with coprime factors of both the plant and the controller subject to simultaneous H-infinity multiplicative or relative perturbations are obtained. (C) 1998 Elsevier Science Ltd. All rights reserved