Unknown input observer for state affine systems - a geometric existence condition

The problem of designing of an unknown input observer for linear systems is widely studied in the literature. Using the geometric approach, an intrinsic characterization permitting to design such an observer is stated in G. Basile and G. Marro (1969), R. Guidorzi and J.S. Marro (1976) and S.P. Bhattacharyya (1978). In this paper an unknown input observer design for a class of state affine systems is considered. As in S.P. Bhattacharyya (1978), a geometric sufficient condition is given in order to design such an unknown input observer.