Delay-Induced Synchronization of Identical Linear Multiagent Systems

This paper studies a class of fast consensus algorithms for a group of identical multiagent systems each described by the linear state-space model. By using both the current and delayed state information, the proposed delay-induced consensus algorithm is shown to achieve synchronization with a faster convergence speed than the standard one when the eigenvalues of the open-loop system, control parameters, the Laplacian matrix of the network, and the delay satisfy certain conditions. In addition, some sufficient or necessary and sufficient conditions are established to guarantee the closed-loop stability of the delay-induced consensus algorithm, where an extra control parameter on the coupling strength is introduced to adjust the convergence speed of the closed-loop system flexibly. We then show that the delay-induced algorithm is robust to the small intrinsic communication or input delays, i.e., the proposed delay-induced consensus algorithm may also produce a faster convergence speed than the standard one even if there exist small intrinsic communication or input delays. Furthermore, we extend the results from the case of an undirected communication topology to those of a directed communication topology and a switching communication topology. Several simulation examples are presented to illustrate the theoretical results.