  This is the last part of four series papers, aiming at stabilization for
signal-input-signaloutput (SISO) linear finite-dimensional systems corrupted by
general input disturbances. A new observer, referred to as Extended Dynamics
Observer (EDO), is proposed to estimate both the state and disturbance
simultaneously. The working mechanism of EDO consists of two parts: The
disturbance with known dynamics is canceled completely by its dynamics and the
disturbance with unknown dynamics is absorbed by high-gain. It is found that
the high-gain is always working as long as the control plant with unknown input
disturbance is observable which is the only assumption for the observer design.
When the disturbance dynamics are completely unknown except some boundedness,
the EDO is reduced to an extension of the well-known extended state observer or
high-gain observer. The main advantage of the developed method is that the
prior information about both the control plant and the disturbance can be
utilized as much as possible. The more the prior information we have, the
better performance the observer would be. An EDO based stabilizing output
feedback is also developed in the spirit of estimation/cancellation strategy.
The stability of the resulting closed-loop system is established and some of
the theoretical results are validated by numerical simulations.
