State observers for a class of bilinear descriptor systems subjected to unmeasurable disturbances

The class of singular bilinear systems (SBS) subjected to unmeasurable disturbances for which there exists an unknown input observer (UIO) with a linear observation error dynamics is characterised. Necessary and sufficient conditions for the existence of this UIO are given. It is shown that the design of such an UIO is equivalent to the design of an UIO for an appropriate singular linear system (SLS). Both full- and reduced-order UIOs are treated.