Second-order node-to-node consensus of nonlinear multi-agent systems via pinning control

This paper investigates the distributed second-order node-to-node consensus problem of multi-agent systems with nonlinear dynamics. The coordination goal to make each follower track the corresponding leader asymptotically where only a small fraction of followers can sense the states of their corresponding leaders. A novel control protocol is introduced. Based on the Lyapunov stability theory and M-matrix theory, some novel and simple criteria are derived for second-order node-to-node consensus of multi-agent systems under the condition that only a small fraction of followers can sense their corresponding leaders. Finally, a numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.