Practical separation principle of singular Caputo fractional-order systems

This paper investigates the output feedback control problem for a class of nonlinear singular Caputo fractional-order systems using a Lyapunov functional approach. To address this problem, a perturbed singular observer is first designed to provide accurate estimates of the unmeasurable system states under Lipschitz-type nonlinear perturbations. Subsequently, a state-feedback controller is developed to achieve global uniform practical Mittag-Leffler stability of the closed-loop system. A major contribution of this work is the establishment of a practical separation principle, which rigorously demonstrates that the proposed state-feedback control law remains effective when implemented using the observer's estimated states. The theoretical findings are validated through two numerical examples.