Descriptor representations without direct feedthrough term

Abstract Descriptor representations are considered that are given by ( E , A , B , C , D ) with D = 0. Minimality under external equivalence is characterized in terms of the matrices E , A , B and C . Also, transformations are given by which minimal ( E , A , B , C ) representations are related under external equivalence. The transformations turn out to be more simple than in the “ D ≠ 0” case. Algorithms for rewriting an ( E , A , B , C , D ) representation in ( E , A , B , C ) form are also given. Finally, a realization procedure is presented for obtaining a minimal ( E , A , B , C ) representation for a system that is given in polynomial matrix fractional form.