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.