**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31242

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

**Authors:**
S. H. Lee,
M. J. Park,
O. M. Kwon

**Abstract:**

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.

**Keywords:**
Multi-Agent,
Lyapunov method,
linear matrix inequalities (LMIs),
kronecker product,
sampled-data

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1100074

**References:**

[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