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Effectiveness and limitation of circle criterion for LTI robust control systems with control input nonlinearities of sector type
Author(s) -
Kiyama Tsuyoshi,
Hara Shinji,
Iwasaki Tetsuya
Publication year - 2005
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.1032
Subject(s) - control theory (sociology) , linear matrix inequality , robust control , nonlinear system , norm (philosophy) , circle criterion , mathematics , lti system theory , control (management) , linear system , mathematical optimization , computer science , exponential stability , mathematical analysis , physics , quantum mechanics , artificial intelligence , political science , law
This paper considers linear time invariant systems with sector type nonlinearities and proposes regional ℒ 2 performance analysis and synthesis methods based on the circle criterion. In particular, we consider the effect of non‐zero initial states and/or an ℒ 2 disturbance inputs on the ℒ 2 norm of a selected performance output. We show that both analysis and synthesis problems can be recast as linear matrix inequality (LMI) optimization problems, where, for synthesis, the outputs of the nonlinear elements are assumed available for control. Moreover, it is shown when the circle criterion does or does not help to improve the performance bound in robust control synthesis when compared with the existing linear analysis method. Copyright © 2005 John Wiley & Sons, Ltd.