Synchronous consensus of double-integrator continuous-time multi-agent systems with switching topologies and time-varying delays

In this paper, we propose a class of second-order continuous-time consensus protocols in networks with bounded communication delay and switching interaction topologies. We present a sufficient condition under which the information states of all agents approach common values. The convergence analysis relies on properties of nonnegative matrices and graph theory and requires that the union of communication graphs has a spanning tree over a bounded period of time. In addition, convergence in leader-following consensus is proved for switching topology and time-varying agents' awareness. Also the appropriate feedback gains are computed via given mathematical relations.