Bounded real lemma for singular linear continuous-time fractional-order systems. (January 2022) - Marir, Saliha; Chadli, Mohammed; Basin, Michael V.
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.