Convergence rate of distributed consensus for second-order multi-agent systems

This paper is concerned with the consensus convergence rate for second order multi-agent systems. First, when both position and velocity are exchanged between neighboring agents, the fastest consensus convergence rate under a given protocol is derived based on the assumption that all the eigenvalues of the Laplacian matrix are real. Next, in the case when only the position information is exchanged between agents, an observer-based protocol is proposed. We show that with a properly chosen observer structure a separation principle can be established, namely, the poles of the closed-loop multi-agent system are the union of the observer poles and the poles of the closed-loop system under full state information exchange. As such, an observer can be designed to achieve the same fastest consensus convergence rate as that for the case with full state information exchange. Simulations are provided to verify the findings and compare with existing methods.