Research on synchronized assets of multiple individuals based on delayed feedback control

From a theoretical perspective, it is worthwhile to use the idea of control to synchronize multiple individual assets. We regard personal assets as multi-agent systems, i.e., second-order multi-agent systems (SOMAS). The delayed feedback control for consensus and average quasi-consensus of delayed SOMAS is studied. First, two weight matrices are studied, where the interactions are not entirely cooperative into the SOMAS with mixed time-varying delays (the delay varies with time). Second, a delayed feedback control is designed based on two weight matrices where the interactions are cooperative to get the consensus about followers and the average quasi-consensus about leader and followers. The consensus and average quasi-consensus of the delayed SOMAS are established by the graph-theoretic technique and Lyapunov functions. Finally, some numerical simulations is given to verify the theory.