Controllability of discrete-time heterogeneous multi-agent systems with time-delay

In this paper, we investigate the controllability of discrete-time heterogeneous multi-agent systems with time-delay and design a class of neighbor-based control protocols. It is established that the rank test and PBH rank test for the discrete-time heterogeneous multi-agent systems with time-delay under fixed topology. Finally, example and numerical simulation are given to demonstrate the effectiveness of the theoretical results.