New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification Problems

Omar Kahouli, Assaad Jmal, Omar Naifar, Abdelhameed M. Nagy and Abdellatif Ben Makhlouf
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Omar Kahouli: Department of Electronics Engineering, Community College, University of Ha’il, Ha’il 2440, Saudi Arabia
Assaad Jmal: Control and Energy Management Laboratory, National School of Engineering, Sfax University, BP 1173, Sfax 3038, Tunisia
Omar Naifar: Control and Energy Management Laboratory, National School of Engineering, Sfax University, BP 1173, Sfax 3038, Tunisia
Abdelhameed M. Nagy: Department of Mathematics, Faculty of Science, Kuwait University, Safat 13060, Kuwait
Abdellatif Ben Makhlouf: Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka 72311, Saudi Arabia

Mathematics, 2022, vol. 10, issue 11, 1-17

Abstract: In the last few years, a new class of fractional-order (FO) systems, known as Katugampola FO systems, has been introduced. This class is noteworthy to investigate, as it presents a generalization of the well-known Caputo fractional-order systems. In this paper, a novel lemma for the analysis of a function with a bounded Katugampola fractional integral is presented and proven. The Caputo–Katugampola fractional derivative concept, which involves two parameters 0 < α < 1 and ρ > 0, was used. Then, using the demonstrated barbalat-like lemma, two identification problems, namely, the “Fractional Error Model 1” and the “Fractional Error Model 1 with parameter constraints”, were studied and solved. Numerical simulations were carried out to validate our theoretical results.

Keywords: fractional-order systems; bounded Katugampola fractional integral; Caputo–Katugampola fractional derivative; identification (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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