A Graphical Characterization of Structurally Controllable Linear Systems with Dependent Parameters
For control theorists, this work generalizes structural controllability to dependent parameters, but the binary assumption limits its applicability.
This paper extends structural controllability to linear systems where parameters may appear in multiple locations of the matrix pair (A, B). Under a binary assumption, it provides a graph-theoretic characterization of such systems.
One version of the concept of structural controllability defined for single-input systems by Lin and subsequently generalized to multi-input systems by others, states that a parameterized matrix pair $(A, B)$ whose nonzero entries are distinct parameters, is structurally controllable if values can be assigned to the parameters which cause the resulting matrix pair to be controllable. In this paper the concept of structural controllability is broadened to allow for the possibility that a parameter may appear in more than one location in the pair $(A, B)$. Subject to a certain condition on the parameterization called the "binary assumption", an explicit graph-theoretic characterization of such matrix pairs is derived.