Frequency assignment maps, relation to system invariants and bounded complexity solutions

Multilinear maps such as those appearing in pole placement problems can be factored into a linear and a standard multilinear map. The rank of the linear one, determines to a great extent the assignability properties of the system. We present a relation between these ranks and the controllability indices when the system has two inputs. In this case if the controllability indices have certain values the corresponding Plucker matrices are always rank deficient. Finally we work out bounds for low complexity solutions based on the rank of the Plucker matrices