CONNECTION OF MULTIPLICATIVE RELATIVE PERTURBATION IN COPRIME FACTORSAND 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 c oprime factors that are not necessarily normalized, is the same as the one described by a gap or upsilon-gap metric ball. Hence all the stab ility robustness results for gap or upsilon-gap metric uncertainty car ry over to this type of coprime factor perturbation. Uncertain systems described by H-infinity multiplicative or relative perturbations in c oprime Factors are also studied in this paper. Necessary and sufficien t conditions for robust stability of a feedback system with coprime fa ctors of both the plant and the controller subject to simultaneous H-i nfinity multiplicative or relative perturbations are obtained. (C) 199 8 Elsevier Science Ltd. All rights reserved.