Geodesic
Computing the $\mathcalH_2$-Norm of a Fractional-Order System Using the State-Space Linear Model
Kragujevac Journal of Mathematics, Tome 47 (2023) no. 4, p. 531 .

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The main purpose of the present paper is to establish an alternative approach to compute the $\mathcal{H}_2$-norm for a fractional-order transfer function of the first kind based on Caputo fractional derivative. The key idea behind this new approach is the use of the concept of the parahermitian transfer matrices and the state-space realization. Numerical examples are presented to illustrate the new approach.
Classification : 15A30, 37N35 26A33, 44A10
Keywords: fractional-order differentiation, fractional transfer function of the first kind, $\mathcalH_2$-norm, parahermitian transfer matrices, state-space linear model, transformation matrices 
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     author = {Aouda Lakeb and Zineb Kaisserli and Djillali Bouagada},
     title = {Computing the $\mathcalH_2${-Norm} of a {Fractional-Order} {System} {Using} the {State-Space} {Linear} {Model}},
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Aouda Lakeb; Zineb Kaisserli; Djillali Bouagada. Computing the $\mathcalH_2$-Norm of a Fractional-Order System Using the State-Space Linear Model. Kragujevac Journal of Mathematics, Tome 47 (2023) no. 4, p. 531 . http://geodesic.mathdoc.fr/item/KJM_2023_47_4_a3/