SOS Approach for Practical Stabilization of Tempered Fractional-Order Power System

Hamdi Gassara, Dhouha Kharrat, Abdellatif Ben Makhlouf (), Lassaad Mchiri and Mohamed Rhaima
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Hamdi Gassara: Laboratory of Sciences and Technich of Automatic Control and Computer Engineering, National School of Engineering of Sfax, University of Sfax, PB 1173, Sfax 3038, Tunisia
Dhouha Kharrat: Modeling, Information, and Systems Laboratory, University of Picardie Jules Verne, UFR of Sciences, 33 Rue St Leu, 80000 Amiens, France
Abdellatif Ben Makhlouf: Department of Mathematics, Faculty of Sciences, Sfax University, BP 1171, Sfax 3038, Tunisia
Lassaad Mchiri: ENSIIE, University of Evry-Val-d’Essonne, 1 Square de la Résistance, 91025 Évry-Courcouronnes, CEDEX, France
Mohamed Rhaima: Department of Statistics and Operations Research, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia

Mathematics, 2023, vol. 11, issue 13, 1-10

Abstract: Fractional systems have been widely utilized in various fields, such as mathematics, physics and finance, providing a versatile framework for precise measurements and calculations involving partial quantities. This paper aims to develop a novel polynomial controller for a power system (PS) with fractional-order (FO) dynamics. It begins by studying the practical stability of a general class of tempered fractional-order (TFO) nonlinear systems, with broad applicability and potential for expanding its applications. Afterward, a polynomial controller is designed to guarantee the practical stability of the PS, encompassing the standard constant controller as a specific instance. The design conditions for this controller are resolved using the sum of squares (SOS) approach, a powerful technique for guaranteeing stability and control design. To showcase the practical value of the analytical findings, simulations of the PS are conducted utilizing SOSTOOLS.

Keywords: fractional calculus; Lyapunov theory; numerical solutions; SOSTOOLS; practical stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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