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ROBUST STABILIZATION IN THE BIBO GAP TOPOLOGY
Author(s) -
Bonnet C.,
Partington J. R.
Publication year - 1997
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/(sici)1099-1239(199705)7:5<429::aid-rnc215>3.0.co;2-g
Subject(s) - robustness (evolution) , coprime integers , metric (unit) , robust control , control theory (sociology) , mathematics , bibo stability , nonlinear system , linear system , topology (electrical circuits) , mathematical optimization , computer science , algorithm , control (management) , engineering , combinatorics , physics , mathematical analysis , biochemistry , chemistry , operations management , quantum mechanics , artificial intelligence , gene
Abstract We consider robust stabilization of both linear causal discrete‐time systems in an l 1 ‐setting and linear causal continuous‐time systems in an L 1 ‐setting. We introduce a new metric in the space of l 1 ( L 1 )‐stabilizable systems in terms of their coprime factorizations. This metric is easily computed and induces the gap topology. We show how robustness optimization in this metric is related to robustness optimization for normalized factor perturbations. In each case, the optimal controller determined by Glover and McFarlane (and studied byGeorgiou and Smith) in the l 2 ( L 2 )‐setting plays an important role. Finally we show that this metric is easily linked to approximation and identification. © 1997 by John Wiley & Sons, Ltd. Int. J. Robust Nonlinear Control, Vol. 7, 429–447 (1997)