State space analysis of disturbance observer and a robust stability condition

In this paper, we analyze the classical linear disturbance observer (DOB) approach in the state space. Our tool for the analysis is the singular perturbation theory. With the tool, an almost necessary and sufficient condition is proposed for robust stability of the closed-loop system with the DOB when the Q-filter has sufficiently large bandwidth. The proposed analysis enlightens the power and the limitations of the classical DOB approach, which have not been well discussed in the literature.