Graph-theoretic Approach to the Generic Structure of Zeros and Poles of Large-scale Systems in Descriptor form

Abstract

For large-scale systems, the state-space description in standard form may not be regarded as an appropriate system representation in most cases. System representations in descriptor form (1), (2) are better suited. However, there may arise new phenomena such as poles and decoupling zeros at infinity. This paper deals with a graphtheoretic approach for investigating poles and zeros of systems in descriptor form. A definition of poles and zeros in terms of the originally given system matrices is a prerequisite of their graphical interpretation (Section 2). Then, the concept of structure matrices and a few graphtheoretic conventions are explained. Finally, important structural properties of zeros and poles are graph-theoretically characterized.