An almost necessary and sufficient condition for robust stability of closed-loop systems with disturbance observer

The disturbance observer (DOB)-based controller has been widely employed in industrial applications due to its powerful ability to reject disturbances and compensate plant uncertainties. In spite of various successful applications, no necessary and sufficient condition for robust stability of the closed loop systems with the DOB has been reported in the literature. In this paper, we present an almost necessary and sufficient condition for robust stability when the Q-filter has a sufficiently small time constant. The proposed condition indicates that robust stabilization can be achieved against arbitrarily large (but bounded) uncertain parameters, provided that an outer-loop controller stabilizes the nominal system, and uncertain plant is of minimum phase.