Parameterization of reduced-order function observers for singular systems

A parameterization of all reduced-order function observers for singular systems is presented. The estimation error dynamics of linear reduced-order function observers are also parameterized for singular systems with unknown input disturbances. It is shown that the design problem of optimal robust observers can be solved by transferring it into the well-known model-matching problem. Our results based on the design of non-minimal order observers are of significance both in generality and in practical applications.