Necessary and sufficient conditions for consensus of third-order multi-agent systems

This paper studies the consensus problem of third-order multi-agent systems for the case of undirected graph. Necessary and sufficient conditions for third-order consensus have been established under three different protocols. Unlike most of existing papers, we here focus on illustrating the relationship between the scaling strengths and the eigenvalues of the involved Laplacian matrix, which guarantees the third-order consensus for three different protocols.