Couple-group consensus of different-order systems with complex relationship

For this paper, we investigate couple-group consensus for the heterogeneous complex systems through pinning controller. A new control protocol is designed utilizing the cooperative-competitive interaction in the system. Aiming at the weakly connected topology, the sufficient criteria and related pinning strategies are obtained via several effective methods such as M matrix, Lyapunov stability theorem and graph theory and so on. The couple-group consensus is achieve on condition that zero in-degree nodes be pinned and the second order agents's pinning gains must satisfy the upper bound condition which we obtained, which is result from this paper. In the end, the availability of the consequences is shown by means of simulations.