Practical Observer Design for Nonlinear Systems using Caputo Fractional Derivative with Respect to Another Function

This paper builds upon our prior work [23], analyzing the study of observer design for nonlinear systems utilizing the Caputo fractional derivative with respect to another function. Two critical nonlinear conditions are employed: the One-Sided Lipschitz (OSL) condition and the quasi-One-Sided Lipschitz (quasi-OSL) condition. These conditions are key to ensuring the practical stability of the system under consideration. The observer is designed with a tuned parameter, θ θ, which is chosen to be a high-gain value, effectively enlarging the set of feasible solutions. While this paper focuses on the theoretical aspects of the observer design, a numerical example remains a future objective, as the numerical approximation of the fractional derivative with respect to another function is still under development.