Distributed proportion-integration-derivation formation control for second-order multi-agent systems with communication time delays

This paper considers the problem of distributed formation control for a second-order multi-agent system with a directed communication topology and constant communication time delays. A distributed proportion-integration-derivation (DPID) formation control law is proposed for the multi-agent system by introducing the integration information of the formation errors. A delay-independent condition and two delay-dependent conditions on the asymptotical formation stability are respectively presented under the assumption of the communication topology containing a directed spanning tree. Based on the Nyquist stability criterion, the range of the feasible time delays for asymptotical formation stability is obtained by analyzing the relationship between the Nyquist curves and the unit circle. Finally, simulations illustrate the effectiveness of the theoretical results.