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The new concepts of "structure" and "structural controllability" for a linear time-invariant control system (described by a pair ( A,b )) are defined and studied. The physical justification of these concepts and examples are also given. The graph of a pair ( A,b ) is also defined. This gives another way of describing the structure of this pair. The property of structural controllability is reduced to a property of the graph of the pair ( A,b ). To do this, the basic concept of a "cactus" and the related concept of a "precactus" are introduced. The main result of this paper states that the pair ( A,b ) is structurally controllable if an only if the graph of ( A,b ) is "spanned by a cactus." The result is also expressed in a more conventional way, in terms of some properties of the pair ( A,b ).
Ching-Tai Lin (Sat,) studied this question.