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${H}_{\infty }$ consensus of second-order multi-agent systems with asymmetric delays. (English) Zbl 1252.93049
Summary: This paper is concerned with the problem of consensus in the ${H}_{\infty }$ sense for second-order continuous-time multi-agent systems with multiple asymmetric time-varying delays. By using a model transformation approach and matrix theory, we establish several conditions in terms of linear matrix inequalities such that consensus of multi-agent systems can be achieved in the ${H}_{\infty }$ sense. The feasibility of the consensus conditions is also analyzed. As an application, we consider the case of intermittent measurement between agents. Numerical examples are presented to illustrate the theoretical results which can be applied to the case of negative information weights.
##### MSC:
 93B36 ${H}^{\infty }$-control 93A14 Decentralized systems
##### References:
 [1] Olfati-Saber, R.; Fax, J. A.; Murray, R. M.: Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE 95, 215-233 (2007) [2] Ren, W.; Beard, R. W.; Atkins, E. M.: Information consensus in multivehicle cooperative control, IEEE control systems magazine 27, 71-82 (2007) [3] Jadbabaie, A.; Lin, J.; Morse, A. S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE transactions on automatic control 48, 988-1001 (2003) [4] L. Moreau, Stability of continuous-time distributed consensus algorithms, Proc. 43rd IEEE Conf. Decision and Control, 2004, pp. 3998–4003. [5] Olfati-Saber, R.; Murray, R. M.: Consensus problems in networks of agents with switching topology and time-delays, IEEE transactions on automatic control 49, 1520-1533 (2004) [6] Ren, W.; Beard, R. W.: Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE transactions on automatic control 50, 655-661 (2005) [7] Moreau, L.: Stability of multiagent systems with time-dependent communication links, IEEE transactions on automatic control 50, 169-182 (2005) [8] Bauso, D.; Giarré, L.; Pesenti, R.: Non-linear protocols for optimal distributed consensus in networks of dynamic agents, Systems control letters 55, 918-928 (2006) · Zbl 1111.68009 · doi:10.1016/j.sysconle.2006.06.005 [9] Lin, Z.; Francis, B.; Maggiore, M.: State agreement for continuous-time coupled nonlinear systems, SIAM journal on control and optimization 46, 288-307 (2007) · Zbl 1141.93032 · doi:10.1137/050626405 [10] Sun, Y. G.; Wang, L.; Xie, G.: Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays, Systems and control letters 57, 175-183 (2008) · Zbl 1133.68412 · doi:10.1016/j.sysconle.2007.08.009 [11] Xiao, F.; Wang, L.: Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays, IEEE transactions on automatic control 53, 1804-1816 (2008) [12] Li, T.; Zhang, J. F.: Mean square average-consensus under measurement noises and fixed topologies: necessary and sufficient conditions, Automatica 45, 1929-1936 (2009) · Zbl 1185.93006 · doi:10.1016/j.automatica.2009.04.017 [13] Sun, Y. G.; Wang, L.: Consensus of multi-agent systems in directed networks with non-uniform time varying delays, IEEE transactions on automatic control 54, 1607-1613 (2009) [14] Munz, U.; Papachristodoulou, A.; Allgower, F.: Delay robustness in consensus problems, Automatica 46, 1252-1265 (2010) · Zbl 1204.93013 · doi:10.1016/j.automatica.2010.04.008 [15] Papachristodoulou, A.; Jadbabaie, A.; Münz, U.: Effects of delay in multi-agent consensus and oscillatory synchronization, IEEE transactions on automatic control 55, 1471-1477 (2010) [16] Olfati-Saber, R.: Flocking for multi-agent dynamic systems: algorithms and theory, IEEE transactions on automatic control 51, 401-420 (2006) [17] Hu, J.; Hong, Y.: Leader-following coordination of multi-agent systems with coupling time delays, Physica A 374, 853-863 (2007) [18] Lin, P.; Ha, Y.; Li, L.: Distributed robust H-infinity consensus control in directed networks of agents with time-delay, Systems and control letters 57, 643-653 (2008) · Zbl 1140.93355 · doi:10.1016/j.sysconle.2008.01.002 [19] Su, H.; Wang, X.: Flocking of multi-agents with a virtual leader, IEEE transactions on automatic control 54, 293-307 (2009) [20] Sun, Y. G.; Wang, L.: Consensus problems in networks of agents with double integrator dynamics and time varying delays, International journal of control 82, 1937-1945 (2009) · Zbl 1178.93013 · doi:10.1080/00207170902838269 [21] Gao, Y. P.; Wang, L.; Xie, G.; Wu, B.: Consensus of multi-agent systems based on sampled-data control, International journal of control 82, 2193-2205 (2009) · Zbl 1178.93091 · doi:10.1080/00207170902948035 [22] Gao, Y. P.; Wang, L.: Consensus of multiple double-integrator agents with intermittent measurement, International journal of robust and nonlinear control 20, 1140-1155 (2010) · Zbl 1200.93094 · doi:10.1002/rnc.1496 [23] Gao, Y. P.; Wang, L.: Asynchronous consensus of continuous-time multi-agent systems with intermittent measurement, International journal of control 83, 552-562 (2010) · Zbl 1222.93009 · doi:10.1080/00207170903297192 [24] 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, 778-784 (2010) [25] Xiao, F.; Wang, L.; Chen, J.: Partial state consensus for networks of second-order dynamic agents, Systems and control letters 59, 775-781 (2010) · Zbl 1217.93020 · doi:10.1016/j.sysconle.2010.09.003 [26] Gu, Y.; Wang, S.; Li, Q.; Cheng, Z.; Qian, J.: On delay-dependent stability and decay estimate for uncertain systems with time-varying delay, Automatica 34, 1035-1039 (1998) · Zbl 0951.93059 · doi:10.1016/S0005-1098(98)00045-4