Abstract
Continuous descriptor systems E x ̇ Ax+Bu , yCx, 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.
Published Version
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