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 1 multiplicative or relative perturbation in its coprime factors that are not necessarily normalized, is the same as the one described by a gap or-gap metric ball. Hence all the stability robustness results for gap or-gap metric uncertainty carry over to this type of coprime factor perturbation. Uncertain systems described by H 1 multiplicative or relative perturbations in coprime factors are also studied in this paper. Necessary and suucient conditions for robust stability of a feedback system with coprime factors of both the plant and the controller subject to simultaneous H 1 multiplicative or relative perturbations are obtained.