Consensusability of linear multi‐agent systems with time delay
Wenying Hou, Minyue Fu, Huanshui Zhang · International Journal of Robust and Nonlinear Control · 2015
Summary This paper studies the consensusability of a continuous‐time linear time‐invariant multi‐agent system (MAS) with time delay in an undirected network withNnodes. We show that the MAS can achieve consensus if and only ifN− 1 time‐delay subsystems associated with the eigenvalues of the Laplacian matrix of the network are simultaneously asymptotically stable. By employing a linear matrix inequality (LMI) method, we present a controller design method for a MAS to reach consensus. We also obtain a bound on the maximum time delay for consensusability for a MAS with first‐order integrator dynamics by using frequency‐domain analysis. Copyright © 2015 John Wiley & Sons, Ltd.