GRAPH-THEORETIC APPROACH TO SYMBOLIC ANALYSIS OF LINEAR DESCRIPTOR SYSTEMS

Continuous descriptor systems Ex = Ax + Bu, y = Cx, where E is a possibly singular matrix, are symbolically analyzed by means of digraphs. Starting with four different digraph characterizations of square matrices and determinants, the author favors the Cauchy-Coates interpretation. Then, an appropriate digraph representation of the matrix pencil (sE - A) is given, which is followed by a digraph interpretation of det(sE - A) and the transfer-function matrix C(sE - A)-1 B. Next, a graph-theoretic procedure is derived to reveal a possibly hidden factorizability of the determinant det(sE - A). This is very important for large-scale systems. Finally, as an application of the derived results, an electrical network is analyzed symbolically.