Delay-induced quasi-consensus in multi-agent dynamical systems

This paper studies delay-induced quasi-consensus in multi-agent dynamical systems. A linear consensus protocol in second-order dynamics is designed where both the current and delayed position information is utilized. The time delay, in a common perspective, can induce periodic oscillations or even chaos to dynamical systems. However, it is surprisingly found in this paper that quasi-consensus in a multi-agent system cannot be reached without the delayed position information under the given protocol while it can be achieved with a relatively small time delay by appropriately choosing the coupling strength. A necessary and sufficient condition for reaching quasi-consensus in multi-agent dynamical systems is then established. It is further shown that quasi-consensus can be achieved if and only if the time delay is less than a critical value which depends on the coupling strengths and the largest eigenvalue of the Laplacian matrix of the network. Finally, a simulation example is given to illustrate the theoretical analysis.