Reliable Consensus Problem for Multi-Agent Systems with Sampled-Data

In this paper, reliable consensus of multi-agent systems
with sampled-data is investigated. By using a suitable
Lyapunov-Krasovskii functional and some techniques such as
Wirtinger Inequality, Schur Complement and Kronecker Product, the
results of such system are obtained by solving a set of Linear Matrix
Inequalities (LMIs). One numerical example is included to show the
effectiveness of the proposed criteria.

• S. H. Lee
• M. J. Park
• O. M. Kwon

• Multi-agent
• Linear Matrix Inequalities (LMIs)
• Kronecker Product
• Sampled-Data
• Lyapunov method.

[1] Q. Ma, Z. Wang, G. Miao, “Second-order group consensus for
multi-agent systems via pinning leader-following approach”, Journal of
the Franklin Institute 351, 2014, pp. 1288–1300.
[2] R.O. Saber, J.A. Fax, R.M. Murray, “Consensus and Cooperation in
Networked Multi-Agent Systems”, Proceedings of the IEEE, vol. 95,
2007, pp. 215-233.
[3] J. Wang, D. Cheng, X, Hu, “Consensus of Multi-agent Linear Dynamic
Systems”, Asian J control, vol. 10, 2008, pp. 144-155.
[4] M.J. Park, K.H. Kim and O.M. Kwon, “Leader-following Consensus
Criterion for Multi-agent Systems with Probabilistic Self-delay”, World
Academy of Science, Engineering and Technology 72, 2012, pp. 244-248.
[5] X. Mu, X. Xiao, K. Liu, J. Zhang, “Leader-following consensus of
multi-agent systems with jointly connected topology using distributed
adaptive protocols”, Journal of the Franklin Institute 351, 2014, pp.
5399-5410.
[6] W. Ren, “Consensus strategies for cooperative control of vehicle
formations”, IET Control Theory Appl., vol. 1, 2007, pp. 505-512.
[7] W. Ren, E. Atkins, “Distributed multi-vehicle coordinated control via
local information exchange”, Int. J. Robust Nonlinear Control, vol. 17,
2007, pp. 1002-1033. [8] A. Jadbabie, J. Lin, A.S. Morse, “Coordination of groups of mobile
autonomous agents using nearest neighbor rules”, IEEE Trans. Autom.
Control, vol. 48, 2003, pp 988-1001.
[9] P. DeLellis, M. DiBernardo, F. Garofalo, D. Liuzza, “Analysis and
stabililty of consensus in networked control systems”, Appl. Math.
Comput, vol. 217, 2010, pp. 988-1000.
[10] L. Hua, Y. Cao, C. Cheng, H. Shao, “Sampled-data control for time-delay
systems”, Journal of the Franklin Institute 339, 2002, pp. 231–238.
[11] C. Peng, T.C. Yang, E.G. Tian, “Brief Paper: Robust fault-tolerant control
of networked control systems with stochastic actuator failure”, IET
Control Theory Appl., Vol. 4, Iss. 12, 2010, pp. 3003–3011.
[12] C.H. Lien, K.W. Yu, Y.F. Lin, Y.J. Chung, L.Y. Chung, “Robust reliable
H_inf control for uncertain nonlinear systems via LMI approach”,
Applied Mathematics and Computation 198, 2008, pp.453–462.
[13] K. H. Kim, M.J. Park, O.M. Kwon, “Reliable control for linear dynamic
systems with time-varying delays and randomly occurring disturbances” ,
The Transactions of the Korean Institute of Electrical Engineers, Vol. 63,
No. 7, 2014, pp. 976-986.
[14] P.G. Park, J.W. Ko, C.K. Jeong, “Reciprocally convex approach to
stability of systems with time-varying delays”, Automatica 47, 2011, pp.
235–238
[15] K. Liu, E. Fridman, “Wirtinger’s inequality and Lyapunov-based
sampled-data stabilization”, Automatica 48, 2012, pp. 102-108
[16] A. Graham, “Kronecker Products and Matrix Calculus: With
Applications”, John Wiley & Sons, Inc., New York, 1982.
[17] K. You, L. Xie, “Coordination of discrete-time multi-agent systems via
relative output feedback,” Int. J. Robust. Nonlinear Control, vol. 21, pp.
1587-1605, 2011.
[18] K. Liu, G. Xie, L. Wang, “Consensus for multi-agent systems under
double integrator dynamics with time-varying communication delays,”
Int. J. Robust. Nonlinear Control, DOI: 10.1002/rnc.1792