## Multi-agent consensus with diverse time-delays and jointly-connected topologies.(English)Zbl 1215.93013

Summary: This paper investigates consensus problems in networks of continuous-time agents with diverse time-delays and jointly-connected topologies. For convergence analysis of the networks, a class of Lyapunov-Krasovskii functions is constructed which contains two parts: one describes the current disagreement dynamics and the other describes the integral impact of the dynamics of the whole network over the past. By a contradiction approach, sufficient conditions are derived under which all agents reach consensus, even though the communication structures between agents dynamically change over time and the corresponding graphs may not be connected. The obtained conditions are composed as a sum of decoupled parts corresponding to each possible connected component of the communication topology. Finally, numerical examples are included to illustrate the obtained results.

### MSC:

 93A14 Decentralized systems 94C15 Applications of graph theory to circuits and networks
Full Text:

### References:

 [1] Bliman, P., & Ferrari-Trecate, G. (2005). Average consensus problems in networks of agents with delayed communications. In Proceedings of IEEE conference on decision and control (pp. 7066-7071). [2] Blondel, V. D., Hendrickx, J. M., Olshevsky, A., & Tsitsiklis, J. N. (2005). Convergence in multiagent coordination, consensus, and flocking. In Proceedings of IEEE conference on decision and control (pp. 2996-3000). [3] Cao, M., Morse, A. S., & Anderson, B. D. O. (2006). Reaching an agreement using delayed information. In Proceedings of IEEE conference on decision and control (pp. 3375-3380). [4] Fang, L., & Antsaklis, P. J. (2005). Information consensus of asynchronous discrete-time multi-agent systems. In Proceedings of the american control conference(pp. 1883-1888). [5] Godsil, C.; Royle, G., Algebraic graph theory, (2001), Springer-Verlag New York · Zbl 0968.05002 [6] Hale, J., Theory of functional differential equations, (1977), Springer-Verlag New York [7] Hong, Y.; Gao, L.; Cheng, D.; Hu, J., Lyapunov-based approach to multiagent systems with switching jointly connected interconnection, IEEE transactions on automatic control, 52, 5, 943-948, (2007) · Zbl 1366.93437 [8] Jadbabaie, A.; Lin, J.; Morse, A.S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE transactions on automatic control, 48, 6, 988-1001, (2003) · Zbl 1364.93514 [9] Lee, D., & Spong, M. W. (2006). Agreement with non-uniform information delays. In Proceedings of the American control conference (pp. 756-761). [10] Liberzon, D., Switching systems and control, (2003), Birkhäuser Boston · Zbl 1036.93001 [11] Li, Z.; Duan, Z.; Chen, G.; Huang, L., Consensus of multi-agent systems and synchronization of complex networks: a unified viewpoint, IEEE transaction on circuits and systems-I, 57, 1, 213-224, (2010) [12] Lin, P.; Jia, Y., Average-consensus in networks of multi-agents with both switching topology and coupling time-delay, Physica A, 387, 1, 303-313, (2008) [13] 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 [14] Lin, P., Jia, Y., Du, J., & Yu, S. (2009). Average consensus for networks of continuous-time agents with delayed information and jointly-connected topologies. In Proceedings of american control conference (pp. 3884-3889). [15] Lin, P.; Jia, Y.; Li, L., Distributed robust $$H_\infty$$ consensus control in directed networks of agents with time-delay, Systems and control letters, 57, 8, 643-653, (2008) · Zbl 1140.93355 [16] Liu, Y.; Passino, K.M., Cohesive behaviors of multiagent systems with information flow constraints, IEEE transactions on automatic control, 51, 11, 1734-1748, (2006) · Zbl 1366.93034 [17] Moreau, L., Stability of multi-agent systems with time-dependent communication links, IEEE transactions on automatic control, 50, 2, 169-182, (2005) · Zbl 1365.93268 [18] Moreau, L. (2004). Stability of continuous-time distributed consensus algorithm. In Proceedings of IEEE conference on decision and control (pp. 3998-4003). [19] Olfati-Saber, R.; Fax, J.A.; Murray, R.M., Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95, 1, 215-233, (2007) · Zbl 1376.68138 [20] Olfati-Saber, R.; Murray, R.M., 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 [21] Ren, W.; Beard, R.W., Consensus seeking in multi-agent systems under dynamically changing interaction topologies, IEEE transactions on automatic control, 50, 5, 655-661, (2005) · Zbl 1365.93302 [22] Ren, W., Beard, R. W., & Atkins, E. M. (2005). A survey of consensus problem in multiagent coordination. In Proceedings of the American control conference(pp. 1859-1864). [23] Sun, Y.; Wang, L.; Xie, G., Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays, Systems and control letters, 157, 2, 175-183, (2008) · Zbl 1133.68412 [24] Tian, Y.; Liu, C., Consensus in networks with diverse input and communication delays, IEEE transactions on automatic control, 52, 9, 2122-2127, (2008) [25] Vicsek, T.; Cziroók, A.; Ben-Jacob, E.; Cohen, O.; Shochet, I., Novel type of phase transition in a system of self-deriven particles, Physical review letters, 75, 6, 1226-1229, (1995)
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.