Eigenstructure Assignment based Output Consensus of Heterogeneous Linear Multi-agent Systems

In this paper, we use the output feedback to design a static controller for the output consensus of the heterogeneous multi-agent systems by using eigenstructure assignment theory. The proposed static controller is designed in two steps. Firstly, for the heterogeneous agents, we take advantage of eigenstructure assignment theory and output feedback theory to design static controller for generating the common internal model. In particular, under certain conditions, we show that the generated internal model has at least one non-negative eigenvalue, which is a common requirement in the study of consensus problems. Secondly, we use the algebraic graph theory and feedback control theory to design a static distributed controller for achieving consensus. We find that when the errors of the output feedback satisfy some certain conditions, the consensus of the heterogeneous multiagent system can be guaranteed by adjusting the Laplacian matrix. Finally, an example with numerical simulation is given to illustrate the correctness of our theoretical results.