Necessary and sufficient condition for average consensus of networked multi-agent systems with heterogeneous time delays
Kazunori Sakurama, Kazushi Nakano · International Journal of Systems Science · 2013
This paper deals with an average-consensus problem of networked multi-agent systems with heterogeneous time delays. First, a necessary and sufficient condition is derived for multi-agent systems to achieve average consensus. This condition is represented in the form of an algebraic condition by using the delay-transition and the delay-weighted Laplacians. Second, a performance criterion is introduced to evaluate multi-agent systems that do not achieve average consensus. The criterion is represented in terms of the norms with respect to the above Laplacians. These results imply that the introduced Laplacians play important roles in analysing multi-agent systems with heterogeneous time delays. The validity of the analysis results is demonstrated by simulations with six-agent systems.