Controllability of discrete-time consensus protocol under fixed and switched leaders

In this work, we consider the controlled discrete-time consensus problem in multi-agent systems, where a subset of agents take on leader roles while the remaining agents perform general consensus protocols with control inputs provided by the leaders. First, we derive necessary and sufficient conditions for the controllability under fixed and switched leaders, respectively. Further, we consider the problem of selecting a subset of followers to connect with leader for yielding fastest converging controlled consensus which can be cast as a convex optimization problem.