Connection of Multiplicative/Relative Perturbation in Coprime Factors and Gap Metric Uncertainty

• Published in: Automatica (Oxford) Vol. 34; no. 5; pp. 603 - 607
• Main Authors: GU, GUOXIANG, QIU, LI
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.05.1998; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control system analysis; Control theory. Systems; coprime factorization; Exact sciences and technology; gap metric; Robust stability; uncertain linear systems; gap metric; Robust stability; uncertain linear systems; coprime factorization; Uncertain system; Linear system; Perturbation; Factorization; Prime number
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/S0005-1098(97)00186-6

In this paper, it is shown that a linear uncertain system described by a certain L ∞ multiplicative or relative perturbation in its coprime factors that are not necessarily normalized, is the same as the one described by a gap or ν-gap metric ball. Hence all the stability robustness results for gap or ν-gap metric uncertainty carry over to this type of coprime factor perturbation. Uncertain systems described by H ∞ 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 ∞ multiplicative or relative perturbations are obtained.