On Structural Controllability of Periodically Switching Networks

In this paper, the structural controllability of periodically switching networks is studied. Based on the n-walk theory, we study the effect of repeating a switching network on its temporal dilation, intersection and temporally independent walks respectively, and some digestible examples are given to illustrate the theoretical results. We conclude that periodically repeating a switching network can only increase or maintain its structural controllability. In addition, for periodically switching networks, we propose an algorithm to judge and calculate the minimum number of periods to achieve structural controllability, and a detailed example is also given to illustrate our algorithm. Our work provides a new perspective to study complex periodically switching networks in the real world.