Controllability and energy-related controllability of multi-agent systems on star topology

This paper studies the controllability and energy-related controllability of multi-agent systems on star topology from an algebraic perspective. By the PBH test and the Gramian matrix test, we establish the necessary and sufficient conditions for the controllability of star networks. Furthermore, we derive the average controllability and average control energy of the star networks. Finally, the validity of the theoretical results is verified through numerical examples and simulations.