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. © 1992.