In this paper we study the observer design problem for descriptor systems w
ith partly unknown inputs. We give necessary and sufficient conditions for
the existence of a solution to the disturbance decoupled estimation problem
with or without stable error spectrum requiring at the same time that the
resulting combined system is regular and of index at most one. All results
are proved based on a condensed form that can be computed using orthogonal
matrix transformations, i.e., transformations that can be implemented in a
numerically stable way. (C) 1999 Elsevier Science B.V. All rights reserved.