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A Unifying Framework for Strong Structural Controllability
This paper deals with strong structural controllability of linear systems. In
contrast to existing work, the structured systems studied in this paper have a
so-called zero/nonzero/arbitrary structure, which means that some of the
entries are equal to zero, some of the entries are arbitrary but nonzero, and
the remaining entries are arbitrary (zero or nonzero). We formalize this in
terms of pattern matrices whose entries are either fixed zero, arbitrary
nonzero, or arbitrary. We establish necessary and sufficient algebraic
conditions for strong structural controllability in terms of full rank tests of
certain pattern matrices. We also give a necessary and sufficient graph
theoretic condition for the full rank property of a given pattern matrix. This
graph theoretic condition makes use of a new color change rule that is
introduced in this paper. Based on these two results, we then establish a
necessary and sufficient graph theoretic condition for strong structural
controllability. Moreover, we relate our results to those that exists in the
literature, and explain how our results generalize previous work.Comment: 11 pages, 6 Figure
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