On the controllability and weight controllability of double integrator consensus systems

We consider controllability of leader-follower networks running a double integrator consensus algorithm, communicating over networks modelled by weighted digraphs. First we give sufficient conditions for the system to be controllable based on connectivity of the corresponding graphs and graph symmetry. We then present the necessary and sufficient conditions for a system to be controllable generically, i.e. for almost all choices of weights. The network is then called weight controllable, a new notion introduced by the author. A new descriptor formulation for the double integrator leader-follower consensus system (LFCS) 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 LFCSs.