Structural control of single-input rank one bilinear systems

A bilinear dynamical system can be used to represent the model of a network in which the state obeys linear dynamics and the input is the edge weight of certain controlled edges in the network. We present algebraic and graph-theoretic conditions for the structural controllability of a class of bilinear systems with a single control where the input matrix is rank one. Subsequently, we use these conditions, given a system state graph, to develop an algorithm to design the location of controlled edges (the input matrix) such that the system is structurally controllable.