Consensus for a Class of Multiagent Systems With Time Delays: A Systematic Study in Parameter Space

This article considers the consensus of a general class of second-order multiagent systems (MASs) with time delays, where the controller is of the common proportional and derivative (PD) type. All the delay and the controller gains are treated as free parameters in this article, and our objective is to develop a parameter-space approach that has not been reported in the literature. First, we adopt the complete stability analysis w.r.t. delay under a given PD controller for the corresponding characteristic equations. Next, we divide the controller parameter plane. For each divided region, the type concerning the consensus property can be qualitatively determined. Combining the above steps, we present a parameter-space approach. By using this approach, we can qualitatively as well as quantitatively identify all the consensus set in the whole space of delay plus controller parameters. Finally, the effectiveness and advantage will be clearly demonstrated by examples.