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Relaxations of parameterized LMIs with control applications
Author(s) -
Tuan H. D.,
Apkarian P.
Publication year - 1999
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(199902)9:2<59::aid-rnc392>3.0.co;2-o
Subject(s) - parameterized complexity , robustness (evolution) , mathematics , control theory (sociology) , regular polygon , class (philosophy) , set (abstract data type) , linear system , relaxation (psychology) , computer science , mathematical optimization , control (management) , algorithm , mathematical analysis , artificial intelligence , psychology , social psychology , biochemistry , chemistry , geometry , gene , programming language
A wide variety of problems in control system theory fall within the class of parameterized Linear Matrix Inequalities (LMIs), that is, LMIs whose coefficients are functions of a parameter confined to a compact set. However, in contrast to LMIs, parameterized LMI (PLMIs) feasibility problems involve infinitely many LMIs hence are very hard to solve. In this paper, we propose several effective relaxation techniques to replace PLMIs by a finite set of LMIs. The resulting relaxed feasibility problems thus become convex and hence can be solved by very efficient interior point methods. Applications of these techniques to different problems such as robustness analysis, or Linear Parameter‐Varying (LPV) control are then thoroughly discussed and illustrated by examples. Copyright © 1999 John Wiley & Sons, Ltd.