摘要：AbstractIn this paper, we examine the maximal delay range for robust consensus by using PID-type control protocol for linear first-order multi-agent systems subject to time-varying delays. We derive explicit lower bounds for guaranteed robust consensus of first-order unstable agents collaborated with each other under PID-type control protocol with time-varying delays, which providea priorithe range of delay over which the multi-agent system is guaranteed to obtain robustly consensus by proportional (P) and proportional-derivative (PD) protocols for undirected graphs respectively The results show how the agent dynamics and graph connectivity may fundamentally limit the range of delay tolerable. They also indicate that the derivative control protocol provides an added benefit to increase the allowable delay range by incorporating the delay variation rate. Finally, the numerical examples are used to illustrate the effectiveness of the proposed theoretical results.
