  A general model-based extended state observer (GMB-ESO) is proposed for
single-input single-output linear time-invariant systems with a given state
space model, where the total disturbance, a lump sum of model uncertainties and
external disturbances, is defined as an extended state in the same manner as in
the original formulation of ESO. The conditions for the existence of such an
observer, however, are shown for the first time as 1) the original plant is
observable; and 2) there is no invariant zero between the plant output and the
total disturbance. Then, the finite-step convergence and error characteristics
of GMB-ESO are shown by exploiting its inherent connection to the well-known
unknown input observer (UIO). Furthermore, it is shown that, with the relative
degree of the plant greater than one and the observer eigenvalues all placed at
the origin, GMB-ESO produces the identical disturbance estimation as that of
UIO. Finally, an improved GMB-ESO with built-in zero dynamics is proposed for
those plants with zero dynamics, which is a problem that has not been addressed
in all existing ESO designs.
