The Strong Stabilization of the State Fractional Derivative for Semi-Linear Systems. (27th July 2022)

• Record Type: Journal Article
• Authors: Zitane, Hanaa; Larhrissi, Rachid
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 10(2022)
• Page Start: 1201
• Page End: 1222
• Publication Date: 2022-07-27
• Subjects: Decay estimate -- minimization control problem -- output feedback stabilization -- Riemann–Liouville derivative -- semi-linear systems; 93C10 -- 93D15 -- 26A33 -- 93C20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2093364
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The purpose of this work is to study the strong stabilization of the state fractional spatial derivative of order q ∈ ( 0, 1 ), for a class of semi-linear dynamical systems. First of all, we establish the existence and the uniqueness of the global solution for such a class of systems. Also, we develop sufficient conditions for the strong stabilization with decay estimate of the state fractional spatial derivative. Moreover, under weaker conditions, we determine an alternative feedback control that ensures the strong stabilization of the considered output. Furthermore, we investigate the fractional output stabilization by considering the minimization of a suitably chosen functional cost. Finally, we present a numerical example to illustrate the applicability of our obtained results.