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H ∞ control for uncertain one‐sided Lipschitz nonlinear systems in finite frequency domain
Author(s) -
Saad Wajdi,
Sellami Anis,
Garcia Germain
Publication year - 2020
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.5101
Subject(s) - control theory (sociology) , frequency domain , lipschitz continuity , attenuation , nonlinear system , mathematics , norm (philosophy) , bounded function , lemma (botany) , mathematical analysis , computer science , control (management) , physics , ecology , poaceae , quantum mechanics , artificial intelligence , law , political science , optics , biology
Summary The current article discusses the H ∞ disturbance attenuation control design problem for one‐sided Lipschitz systems in finite frequency domain. Models containing norm‐bounded parameter uncertainties, disturbances, and input nonlinearities are considered. By contrast to existing full frequency methods, the H ∞ controller is computed depending on the frequency ranges of disturbances. The finite frequencyℒ 2disturbance attenuation index is initially defined. Thanks to Finsler's lemma, sufficient and less conservative analysis conditions are also derived for the closed‐loop system. Then, synthesis conditions in the low, middle, and high frequency ranges as well as the whole frequency range, are formulated in terms of linear matrix inequalities. At last, to prove the effectiveness and the superiority of the proposed approach, a physical example is used and a comparative study is done.