Scaled cluster consensus of discrete-time multi-agent systems with general directed topologies

Abstract

ABSTRACTThis note proposes a notion of scaled cluster consensus, wherein the final consensus states within different clusters converge to prescribed ratios. Unlike most results in existing literature on cluster consensus, no constraints are imposed on the system topologies under the designed protocol, i.e. the agents are not required to possess any cluster affiliation information of others. For the delay-free case, an explicit scaled cluster consensus function is provided by exploring the characteristics of stochastic matrices. Diverse input delays and asymmetric communication delays are both considered, and sufficient condition for scaled cluster consensus is derived based on frequency domain analysis. Finally, numerical examples are given to illustrate the effectiveness of the presented results.