H∞ control for uncertain one‐sided Lipschitz nonlinear systems in finite frequency domain. (7th July 2020)

• Record Type: Journal Article
• Authors: Saad, Wajdi; Sellami, Anis; Garcia, Germain
• Is Part Of: International journal of robust and nonlinear control. Volume 30:Number 14(2020)
• Page Start: 5712
• Page End: 5727
• Publication Date: 2020-07-07
• Subjects: H∞ -- finite frequency -- nonlinear systems -- one‐sided Lipschitz -- robust control; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.5101
• Languages: English
• ISSNs: 1049-8923

Abstract

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 frequency ℒ 2 disturbance 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.