Bounded real lemma for singular linear continuous-time fractional-order systems. (January 2022)

• Record Type: Journal Article
• Authors: Marir, Saliha; Chadli, Mohammed; Basin, Michael V.
• Is Part Of: Automatica. Volume 135(2022)
• Publication Date: 2022-01
• Subjects: Fractional-order systems -- Singular systems -- Admissibility -- Bounded real lemma -- LMIs; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2021.109962
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper proposes novel necessary and sufficient strict linear matrix inequalities ( LMI s ), to characterize admissibility of singular fractional-order linear continuous-time systems with the fractional derivative of order α belonging to 1 ≤ α < 2 . Then, the problem of the bounded real lemma corresponding to the H ∞ norm computation is addressed involving additional variables. Necessary and sufficient conditions are established via a set of LMI s that can be effectively used to design H ∞ controllers. Based on the corresponding bounded real lemma, a state feedback control with a prescribed H ∞ performance index for the underlying systems is proposed. Finally, numerical examples are provided to show effectiveness of the given results.