Leader-Following Consensus Criterion For Multi-Agent Systems With Probabilistic Self-Delay

• Main Authors: M.J. Park, K.H. Kim, O.M. Kwon
• Format: Text
• Language: English
• Published: Zenodo 2012
• Subjects: Multi-agent systems; probabilistic self-delay; consensus; Lyapunov method; LMI.; Morse; morse; ren
• Online Access: https://dx.doi.org/10.5281/zenodo.1077495; https://zenodo.org/record/1077495

This paper proposes a delay-dependent leader-following consensus condition of multi-agent systems with both communication delay and probabilistic self-delay. The proposed methods employ a suitable piecewise Lyapunov-Krasovskii functional and the average dwell time approach. New consensus criterion for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical example showed that the proposed method is effective. : {"references": ["R.O. Saber, J.A. Fax, R.M. Murray, \"Consensus and Cooperation in\nNetworked Multi-Agent Systems\", Proceedings of The IEEE, vol. 95,\n2007, pp. 215-233.", "J. Wang, D. Cheng, X. Hu, \"Consensus of Multi-agent Linear Dynamic\nSystems\", Asian J Control, vol. 10, 2008, pp. 144-155.", "W. Ren, \"Consensus strategies for cooperative control of vehicle formations\",\nIET Control Theory Appl., vol. 1, 2007, pp. 505-512.", "W. Ren, E. Atkins, \"Distributed multi-vehicle coordinated control via\nlocal information exchange\", Int. J. Robust Nonlinear Control, vol. 17,\n2007, pp. 1002-1033.", "A. Jadbabie, J. Lin, A.S. Morse, \"Coordination of groups of mobile\nautonomous agents using nearest neighbor rules\", IEEE Trans. Autom.\nControl, vol. 48, 2003, pp 988-1001.", "P. DeLellis, M. DiBernardo, F. Garofalo, D. Liuzza, \"Analysis and\nstabililty of consensus in networked control systems\", Appl. Math.\nComput., vol. 217, 2010, pp. 988-1000.", "D. Lee, M.W. Spong, \"Stable Flocking of Multiple Inertial Agents on\nBalanced Graphs\", IEEE Trans. Autom. Control, vol. 52, 2007, pp. 1469-\n1475.", "H. Kim, H. Shim, J.H. Seo, \"Output Consensus of Heterogeneous\nUncertain Linear Multi-Agent Systems\", IEEE Trans. Autom. Control,\nvol. 56, 2011, pp. 200-206.", "J.P. Hu, Y.G. Hong, \"Leader-following coordination of multi-agent systems\nwith coupling time delay\", Physica A, vol. 374, 2007, pp. 853-863.\n[10] Y.P. Tian, C.L. Liu, \"Consensus of Mulit-Agnet Systems With Diverse\nInput and Communication Delays\", IEEE Trans. Autom. Control, vol.\n53, 2008, pp. 2122-2128.\n[11] F. Xiao, L. Wang, \"State consensus for multi-agent systems with\nswitching topologies and time-varying delays\", Int. J. Control, vol. 79,\n2006, pp. 1277-1284.\n[12] J. Qin, H. Gao, W.X. Zheng, \"On average consensus in directed networks\nof agents with switching topology and time delay\", Int. J. Syst. Sci., vol.\n42, 2011, pp. 1947-1956.\n[13] S. Xu, J. Lam, \"A survey of linear matrix inequality techniques in\nstability analysis of delay systems\", Int. J. Syst. Sci., vol. 39, 2008,\npp. 1095-1113.\n[14] D. Liberzon, Switching in Systems and Control, Birkh\u252c\u00bfauser, Boston;\n2003.\n[15] S. Boyd, L.E. Ghaoui, E. Feron E, V. Balakrishnan, Linear Matrix\nInequalities in System and Control Theory, SIAM, Philadelphia; 1994.\n[16] Z.G. Wu, Ju H. Park, H. Su, J. Chu, \"Robust dissipativity analysis\nof nerual networks with time-vayring delay and randomly occurring\nuncertainties\", Nonlinear Dyn., doi:10.1007/s11071-012-0350-1.\n[17] J. Hu, Z. Wang, H. Gao, L.K. Stergioulas, \"Robust sliding mode\ncontrol for discrete stochastic systems with mixed time delays, randomly\noccurring uncertainties, and randomly occurring nonliearities\", IEEE\nTrans. Ind. Electron., vol. 59, 2012, pp. 3008-3015.\n[18] C. Godsil and G. Royle, Algebraic Graph Theory, Springer-Verlag, New\nYork; 2001.\n[19] W. Ni, D. Cheng, \"Leader-following consensus of multi-agent systems\nunder fixed and switching topologies\", Syst. Contr. Lett., vol. 59, 2010,\npp. 209-217.\n[20] M.C. de Oliveira, R.E. Skelton, Stability tests for constrained linear\nsystems, Springer-Verlag, Berlin; 2001, pp. 241-257.\n[21] K. Gu, \"An integral inequality in the stability problem of time-delay\nsystems\", in Proceedings of the 39th IEEE Conference on Decision and\nControl, Sydney, Australia, 2000, pp. 2805-2810.\n[22] S.H. Kim, P. Park, C.K. Jeong, \"Robust H\u221e stabilisation of networks\ncontrol systems with packet analyser\", IET Control Theory Appl., vol. 4,\n2010, pp. 1828-1837.\n[23] X.-M. Sun, J. Zhao, D.J. Hill, \"Stability and L2-gain analysis for\nswitched delay systems: A delay-dependent method\", Automatica, vol.\n42, 2006, pp. 1769-1774.\n[24] D. Zhang, L. Yu, \"Exponential stability analysis for neutral switched\nsystems with interval time-varying mixed delays and nonlinear perturbations\",\nNonlinear Anal.-Hybrid Syst., vol. 6, 2012, pp. 775-786."]}