On the weight controllability of consensus algorithms

In this paper we consider controllability of leader-follower networks running a consensus algorithm. We allow the communication links between the agents to be weighted and give the necessary and sufficient conditions for a the system to be controllable generically, i.e. for almost all choices of weights. We call such a network weight controllable, a new notion that is introduced in this paper. A new descriptor formulation for the leader-follower consensus algorithm is derived that allows modelling communication weights as free parameters without changing the system structure. This leads us to obtaining necessary and sufficient conditions for weight controllability of leader-follower consensus algorithms.