On structural controllability of complex networks using polar placement

The topology of a network can be described as an adjacent matrix A, and structural controllability can be determined. The number of driven nodes, which implies how many different input signals are needed to control the network, can be calculated. In this paper, by replacing the poles of the network, the adjacency matrix A would be changed. By placing poles in different locations, the effects on the proportion of driven nodes are discussed. We find that, for a network with a controllable canonical form, the driven nodes number would not be affected, which means that considering the driven nodes number, the structural controllability would not be weaken. Moreover, with proper poles location, the number of non-zero elements in the feedback matric would be reduced which leads to lower cost. And these poles guarantees stability and transient response of the complex network.