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Second-order consensus of multi-agent systems with linear dynamics

This paper considers a second-order consensus problem for linear multi-agent systems with directed topology. In the systems, each agent can be controlled by controlling its position and velocity. To reach the consensus of the systems, the feedback gain is designed in the control input of the consensus protocol. The control input of each agent is influenced by its position and velocity. There is a directed spanning tree in the corresponding communication topology. This condition is general and weak. Some sufficient conditions are obtained to solve the consensus problem. At last, a simple case is given to verify the efficacy of the proposed controller.