Second-order group consensus in multi-agent systems with time-delays based on second-order neighbours´ information

This paper mainly investigates the second-order group consensus for multi-agent systems with or without time-varying delays based on using the second-order neighbours´ information. For the case without time-delays, it is shown that the sufficient conditions in form of Kronecker product can be obtained to achieve the given group consensus if the two subnetworks G1, G2 of virtual network G are balanced couple. The error system is adopted to solve the group consensus problems for multi-agent systems with time-varying delays. The ultimate results are worked out by Lyapunov functions. Finally, some illustrate examples are proved to demonstrate the effectiveness of the theoretical findings.