Control configuration design for a class of structural bilinear systems

Analysis of structured systems has opened up the potential to understand the control properties of large-scale systems modeled as networks. Networks present novel questions to control theory because the interchangeability of nodes means that any subset could be controlled. In contrast, classic control systems have prescribed connections between controls and states. We present an algorithm to determine the structure of the input connectivity for single-input rank-one structured bilinear systems, which is analogous to designing the control configuration, or placement, of controls on edges in the network. In particular, we develop the control configuration with a minimum number of new interconnections (with respect to a cacti representation of the graph). These controls become the weights of certain edges in the network representation of the bilinear system.