Cluster Tracking Performance Analysis of Linear Heterogeneous Multi-Agent Networks: A Complex Frequency Domain Approach

This paper presents a complex frequency domain approach to investigate the cluster tracking performance of linear heterogeneous multi-agent networks. Firstly, a designed graph matrix is given to eliminate the interaction influence between coupled subnetworks with different tracking signals. On this basis, the cluster tracking performance analysis problem is decomposed into two parts, i.e., stability analysis and steady-state performance analysis of multi-agent networks. Secondly, based on the network structure, a minimum separable subgraph set is proposed to transform the stability of the multi-agent network into the stability of the separable subnetworks. Further, a signal flow diagram is introduced to solve the stability of the separable subnetworks. Thirdly, in view of Final-value theorem, a necessary and sufficient condition is proposed for achieving the cluster tracking control for the closed-loop stable multi-agent network. This result provides a strong theoretical basis for the flexible design of controllers due to that it quantitatively reveals the inherent law of steady-state performance for multi-agent networks. Finally, an algorithm is established to calculate the steady-state error of a general directed multi-agent network. Some simulations are provided to demonstrate the effectiveness of the theoretical results.