Existence conditions for unknown input functional observers

Abstract

This article presents necessary and sufficient conditions for the existence and design of an unknown input Functional observer. The existence of the observer can be verified by computing a nullspace of a known matrix and testing some matrix rank conditions. The existence of the observer does not require the satisfaction of the observer matching condition (i.e. Equation (16) in Hou and Muller 1992 Hou, M and Muller, P. 1992. Design of Observers for Linear Systems with Unknown Inputs. IEEE Transactions on Automatic Control, 37: 871–875. [Crossref], [Web of Science ®] , [Google Scholar], ‘Design of Observers for Linear Systems with Unknown Inputs’, IEEE Transactions on Automatic Control, 37, 871–875), is not limited to estimating scalar functionals and allows for arbitrary pole placement. The proposed observer always exists when a state observer exists for the unknown input system, and furthermore, the proposed observer can exist even in some instances when an unknown input state observer does not exist.