@article{Alanazi2024, 
author = {Kareem Alanazi and Omar Naifar and Raouf Fakhfakh and Abdellatif Ben Makhlouf},
title = {Innovative observer design for nonlinear systems using Caputo fractional derivative with respect to another function},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {35533-35550},
keywords = {observer-based control, practical stability, CFD with respect to another function, control, observer},
url = {https://www.sciopen.com/article/10.3934/math.20241686},
doi = {10.3934/math.20241686},
abstract = {This work introduces a novel control framework using the Caputo fractional derivative (CFD) with respect to another function—a derivative that has not been thoroughly treated in control theory. By extending the widely recognized Caputo-Hadamard (CH) fractional-order derivative, we address its utility in nonlinear systems. The core of our contribution is the practical stability for systems governed by this derivative, which ensures convergence toward a bounded region around the origin. Additionally, we extend the Lipschitz condition (LC) to the one-sided Lipschitz (OSL) condition for observer design and observer based-control design in fractional-order systems, ensuring its practical stability. Finally, three numerical examples validate the effectiveness of our proposed framework, providing practical insights for control theory advancements.}
}