Delay Range for Consensus Achievable by Proportional and PD Feedback Protocols With Time-Varying Delays

• Published in: IEEE transactions on automatic control Vol. 67; no. 6; pp. 3212 - 3219
• Main Author: Ma, Dan
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Delay; Delays; Eigenvalues and eigenfunctions; Graph theory; Lower bounds; Maximal delay range; Multiagent systems; PD control; Power system dynamics; Proportional derivative; proportional-derivative (PD) protocol; Protocols; robust consensus; Robustness; Time varying control; time-varying delay; Topology
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2021.3096899

This article examines the delay range for robust consensus of unstable first-order agents by using proportional (P) and proportional-derivative (PD) control protocols subject to time-varying delays. The maximal delay range is defined by the delay consensus margin (DCM), which is a robustness measure within which consensus can be achieved robustly despite the presence of uncertain and time-varying delays. We apply an <inline-formula><tex-math notation="LaTeX">H_\infty</tex-math></inline-formula>-type small-gain analysis to multiagent systems, which results in explicit lower bounds on the DCM for both undirected and directed graphs. The results provide sufficient conditions for robust consensus for all time-varying delays that may vary within the range. It is seen that the agent dynamics and the graph connectivity may fundamentally limit the range of tolerable delays. It is also found that the DCM can be increased beyond that achieved by the P protocol by incorporating the delay variation rate in the design of the PD control protocol.