We study the stability characteristic of the active disturbance rejection control for a nonlinear, time-varying plant. To this end, the closed-loop system is reformulated in a form that allows the singular perturbation method to be applied. Since singular perturbation approach enables the decomposition of the original system into a relatively slow subsystem and a relatively fast subsystem, the composite Lyapunov function method is used to determine the stability properties of the decomposed subsystems. Our result shows that the system is exponentially stable, upon which a lower bound for the observer bandwidth is established.