Disturbance observers for general exogenous disturbances

We examine a parameterization of linear disturbance observers for general exogenous disturbances. Using the states and inputs of the system as variables, we got an parameterization of linear disturbance observers for general exogenous disturbances in frequency domain formulation. By comparing with a traditional linear disturbance observer for general exogenous disturbances in time domain formulation, we found that the traditional disturbance observer can be regarded as a specific formulation of the disturbance observer designed by us, therefore the validity of our disturbance observer should could be confirmed. We will show an numerical example to confirm the validity of our method. In another work, we have proposed a parameterization of linear disturbance observers for constant disturbances individually. Because constant disturbances can be regarded as a special case for general exogenous disturbances, we think our disturbance observer for general exogenous disturbances also could be used to estimate constant disturbances. We will offer numerical examples to confirm the guess too. Let aside of rapidity, the validity of our parameterization is undoubted.