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Multiobjective control via successive over‐bounding of quadratic terms
Author(s) -
Shimomura Takashi,
Fujii Takao
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.997
Subject(s) - bounding overwatch , mathematics , quadratic equation , linear matrix inequality , set (abstract data type) , mathematical optimization , bilinear interpolation , control (management) , inequality , order (exchange) , matrix (chemical analysis) , control theory (sociology) , computer science , statistics , mathematical analysis , geometry , artificial intelligence , materials science , finance , economics , composite material , programming language
This paper addresses less conservative control design for multiple design specifications. Problems are described by a set of linear matrix inequalities (LMIs) and solved with non‐common LMI solutions in order to reduce the conservatism arising from seeking a common LMI solution in the past results. Noticing that completing the square can split two variables in bilinear matrix inequality (BMI) terms into two different LMI ones, we propose an iterative algorithm in which non‐positive quadratic terms are successively replaced by their upper bounds. An illustrated example is included. Copyright © 2005 John Wiley & Sons, Ltd.