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Robust stability and performance analysis for uncertain linear systems—The distance measure approach
Author(s) -
Lanzon Alexander,
Engelken Sönke,
Patra Sourav,
Papageorgiou George
Publication year - 2011
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1754
Subject(s) - multiplicative function , stability (learning theory) , measure (data warehouse) , robust control , computation , contrast (vision) , mathematics , robustness (evolution) , inverse , mathematical optimization , small gain theorem , computer science , control theory (sociology) , algorithm , control (management) , engineering , control system , data mining , artificial intelligence , machine learning , mathematical analysis , biochemistry , chemistry , geometry , gene , electrical engineering
SUMMARY This paper presents readily applicable distance measures, robust stability margins and associated robust stability and robust performance theorems for three commonly used uncertainty structures (additive, input/output multiplicative, output/input inverse multiplicative). Besides providing robust stability results for a larger uncertainty class than previously reported (ℛℒ ∞ instead of ℛℋ ∞ ), this paper also states robust performance theorems for the above uncertainty structures. In contrast to previous methods for robust performance analysis, they only require the computation of two infinity norms for every uncertain plant considered. The theorems in this paper enable practising engineers to choose the most suitable uncertainty structure for a family of uncertain plants, as illustrated through a physically motivated numerical example. Copyright © 2011 John Wiley & Sons, Ltd.