# zbMATH — the first resource for mathematics

Input delay margin for consensusability of multi-agent systems. (English) Zbl 1360.93065
Summary: In this paper, we are concerned with the consensus of multi-agent systems with input delay. Among all standard static protocols that achieve the consensus for the multi-agent system under no input delay, we aim to find the maximum input delay such that the system remains consensusable under the same protocols. In the case of continuous-time systems, in view of the continuity of stability with respect to the time delay, the maximum delay margin for consensusability is given for scalar systems and vector systems with a single unstable open-loop pole. For scalar discrete-time systems, we show that the maximum delay margin for consensusability is strictly greater than zero if and only if the open-loop pole of the system is located in a specified interval.

##### MSC:
 93A14 Decentralized systems 93B60 Eigenvalue problems 68T42 Agent technology and artificial intelligence
Full Text:
##### References:
 [1] Gaudette, D. L.; Miller, D. E., When is the achievable disctere time delay margin non-zero?, IEEE Transactions on Automatic Control, 56, 4, 886-890, (2011) · Zbl 1368.93537 [2] Gu, K.; Kharitonov, V. L.; Chen, J., Stability of time-delay systems, (2003), Birkhauser Verlag AG Basel, Switzerland · Zbl 1039.34067 [3] Li, S.; Wang, J.; Luo, X.; Guan, X., A new framework of consensus protocol for complex multi-agent systems, System & Control Letters, 60, 1, 19-26, (2011) · Zbl 1207.93005 [4] Lin, P.; Jia, Y., Consensus of a class of second-order multi-agent systems with time-delay and jointly-connected topologies, IEEE Transactions on Automatic Control, 55, 3, 778-784, (2010) · Zbl 1368.93275 [5] Liu, Y., & Zhu, J. (2008). Consensus of multiagent networks with time delay. Fourth international conference on natural computation (pp. 335-338). [6] Ma, C.; Zhang, J., Necessary and sufficient conditions for consensusbility of linear multi-agent system, IEEE Transactions on Automatic Control, 55, 5, 1263-1268, (2010) · Zbl 1368.93383 [7] Michiels, W.; Engelborghs, K.; Vansevenant, P.; Roose, D., Continuous pole placement for delay equations, Automatica, 38, 5, 747-761, (2002) · Zbl 1034.93026 [8] Middleton, R. H.; Miller, D. E., On the achievable delay margin using LTI control for unstable plants, IEEE Transactions on Automatic Control, 52, 7, 1194-1207, (2007) · Zbl 1366.93446 [9] Münz, U. (2010). Delay robustness in cooperative control. Ph.D. Thesis. Institut für Systemtheorie Regelungstechnik, Universität Stuttgart. [10] Münz, U.; Papachristodoulou, A.; Allgöwer, F., Delay robustness in consensus problems, Automatica, 46, 8, 1252-1265, (2010) · Zbl 1204.93013 [11] Olfati-Saber, R.; Murray, R., Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 49, 9, 1520-1533, (2004) · Zbl 1365.93301 [12] Ren, W.; Beard, R. W., Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE Transactions on Automatic Control, 50, 5, 655-661, (2005) · Zbl 1365.93302 [13] You, K.; Xie, L., Network topology and communication data rate for consensusability of discrete-time multi-agent systems, IEEE Transactions on Automatic Control, 56, 10, 2262-2275, (2011) · Zbl 1368.93014 [14] Zhu, W.; Cheng, D., Leader-following consensus of second-order agents with multiple time-varying delays, Automatica, 46, 12, 1994-1999, (2010) · Zbl 1205.93056
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.