A graph-theoretic characterization for the rank of the transfer matrix of structured system. (English) Zbl 0747.93030

This paper considers structured state space systems \((A,B,C)\) where the entries of the matrices \(A\), \(B\), \(C\) are either zero or independent real parameters. For these systems it is shown that the generic rank of the transfer function \(C(sI_ n=A)^{-1}B\) is equal to the maximum number of vertex disjoint paths from the set of input vertices to the set of output vertices in the associated (directed) system graph. The result is then applied to obtain a necessary and sufficient condition for the generic solvability of the almost disturbance decoupling problem (for structured systems with a structured disturbance input matrix).


93C05 Linear systems in control theory
93B99 Controllability, observability, and system structure
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