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Journal of Applied Nonlinear Dynamics 7(1) (2018) 73--79 | DOI:10.5890/JAND.2018.03.006

Y. Boukal$^{1}$,$^{2}$,$^{3}$, M. Darouach$^{1}$, M. Zasadzinski$^{1}$, N.E. Radhy$^{2}$

$^{1}$ Université de Lorraine, Centre de Recherche en Automatique de Nancy (CRAN UMR-7039, CNRS), IUT de Longwy, 186 rue de Lorraine 54400, Cosnes et Romain, France

$^{2}$ Université Hassan II, Faculté des Sciences Ain-Chock, Laboratoire Physique et Matériaux Microélectronique Automatique et Thermique BP: 5366 Maarif, Casablanca 20100, Morocco

$^{3}$ Université de Valenciennes, CNRS, UMR 8201, LAMIH, Laboratoire d'Automatique de Mécanique et d'Informatique Industrielles et Humaines, 59313 Valenciennes, France

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Abstract

This note considers the work entitled “Unknown Input Observer Design for Linear Fractional-Order Time-Delay Systems”. In the above paper [1], the authors gave the existence conditions of such observer, then based on the fractional order Lyapunov stability approach, a sufficient condition for the asymptotic stability of the estimation error have given in a linear matrix inequality (LMI) formulation which is incorrect. In this note, we give the correction of Theorem 7. The new proposed Theorem can be applied to a large kind of delayed fractional-order-system when the delay is time varying or constant, while the above mentioned paper consider only a constant time delay. The proof is based on the diffusive representation of the fractionalorder derivative and the indirect Lyapunov approach proposed in [2].

References

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