Linear observer design using the inverse method for systems with matched disturbances

The paper deals with a state observer design for linear systems with disturbances that lie in the control space. We propose a pseudo output, Σ(t), to be included in the observer. It is found that this pseudo output can be related to the measurable output, y(t), by a dynamic mapping which is invariant of the disturbances. Using the inverse method, Σ(t) can be retrieved by y(t) such that the inaccessible system state can further be estimated by means of the proposed dynamic mapping.