Consensus of second-order multi-agent systems with nonlinear dynamics and time delay

This paper aims at investigating the second-order consensus problem of the multi-agent systems with nonlinear dynamics. Since it is more difficult to obtain the velocity information compared with the position information in practical application, a very simple sufficient condition for updating the coupling gain of the velocity information exchange between each agent is firstly derived to achieve asymptotic consensus. Furthermore, communication delay of each agent is considered for velocity information exchange. The velocity signal from a virtual leader is introduced to reach the second-order consensus. All the above fundamental consensus criteria are guaranteed base on algebraic graph theory, matrix theory, and Lyapunov stability method. Two simulation examples are provided to demonstrate the effectiveness of the analytical results. The results obtained in this paper can be easily applied to various cases, which can facilitate practical designs for the second-order consensus.