A root locus approach to near-controllability of a class of discrete-time bilinear systems with applications to Hermitian matrices

In this paper, a root locus approach is developed to investigate near-controllability of a class of discrete-time bilinear systems and new representations of Hermitian matrices are derived. The root locus approach has three merits: firstly, it makes the proof of near-controllability of the systems more simple; secondly, the control inputs that achieve the state transition can be computed in an explicit way and, meanwhile, the number of the required control inputs can be fixed; and thirdly, it leads to a more general conclusion on near-controllability. A numerical example is given to demonstrate the effectiveness of the root locus approach. Finally, the more general conclusion yields new representations of Hermitian matrices.