In this paper we consider a structured linear system represented by means of a directed graph. We present a graph theoretic method to compute the generic number of invariant zeros of the corresponding Rosenbrock matrix. The method is based on a fundamental decomposition of the directed graph representing the structured system. The generic number of invariant zeros is important in generic versions of problems involving controllability and pole placement.
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Jacob van der Woude (1999) studied this question.
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