Extended Dynamics Observer for Linear Systems with Disturbance

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.