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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.
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https://hal.archives-ouvertes.fr/hal-03389163
Contributor : Frédéric Davesne Connect in order to contact the contributor
Submitted on : Wednesday, October 20, 2021 - 10:34:13 PM
Last modification on : Thursday, October 21, 2021 - 5:30:25 AM

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

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