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Journal Articles Automatica Year : 2022

Bounded real lemma for singular linear continuous-time fractional-order systems

Abstract

This paper proposes novel necessary and sufficient strict linear matrix inequalities (LMIs), 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 LMIs 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.

Domains

Automatic

Dates and versions

hal-03389163 , version 1 (20-10-2021)

Identifiers

Cite

Saliha Marir, Mohammed Chadli, Michael Basin. Bounded real lemma for singular linear continuous-time fractional-order systems. Automatica, 2022, 135, pp.109962. ⟨10.1016/j.automatica.2021.109962⟩. ⟨hal-03389163⟩
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