The use of high-gain observers in nonlinear control to compensate for uncertainties, disturbances and modeling errors, has a long history, see the tutorial paper [1] and papers in the special issue [2]. For instance, Khalil and Freidovich [3] use high-gain observer to compensate for the effects of the disturbances and uncertainties and recover the performance of feedback-linearization-based designs in an output feedback-based setting. The related use of observers to deal with uncertainties and alleviate the need for precise model is also pursued in active disturbance rejection control, see Ref. [4] which covers this technique, references, and links with related approaches. The filtered dynamic inversion controller is shown to provide command following and disturbance rejection for minimum phase uncertain time-invariant systems affected by unknown time-dependent disturbances in Ref. [5]. Liu and Peng [6] study the integration of a disturbance observer, based on an assumption of an additive time-dependent disturbance, into control systems for robot manipulators and provide stability analysis results for the case when the disturbance is constant. The book by Chen and Patton [7] considers the use of input disturbance observer (IDO) for fault detection. From the practical perspective, the IDO-based control has the potential to reduce the time and effort necessary for model-based controller design and calibration by reducing the need to use accurate models [8] as the uncertainty and model errors are compensated by IDO. Main implementation requirements for successful application of IDO-based control involve accurate measurement of system states and outputs, sufficiently high sampling frequency, sufficient actuator authority, and suitable structural properties of the system such as minimum phase characteristics.