Consensusability of multi-agent systems with constant communication delay

This paper focus on the consensusability of high-order multi-agent systems (MASs) with uniform constant communication delay in an undirected network. We show that N agents achieve consensus if and only if N − 1 time-delay subsystems associated with the eigenvalues of the Laplacian matrix are simultaneously asymptotically stable. By employing a linear matrix inequality (LMI) method, we present a sufficient condition for MASs to reach consensus. Also we consider the consensus condition of first-order integrator system by using frequency domain analysis.