Controllability of consensus of multi-agent networks over heterogeneous dynamics

This work investigates controllability issues under the leader-follower framework of consensus problem on multi -agent networks where its agents exhibit the heterogeneous dynamics involving first-, second-, and third -order integrator agents on a continuous time -scale. The communication topology is directed, time -invariant, and the reliability of all interactions are unity. We employ two kinds of consensus protocols that are linear and distributed. The necessary and sufficient criteria for the controllability of followers' dynamics through the selected leaders are obtained in terms of matrix -rank conditions. We also obtain some necessary conditions of controllability involving eigenvectors of system matrices. It is verified that, if either of the first-, second-, or third -order integrator agents are absent, then the controllability of the network becomes equivalent to the controllability of the communication topology just like those of the networks with homogeneous dynamic agents. Obtained results are verified with illustrative examples.