Leader–following consensus control for networked multi-teleoperator systems with interval time-varying communication delays

doi:10.1088/1674-1056/22/7/070506

Abstract We study the leader–following consensus stability and stabilization of networked multi-teleoperator systems with interval time-varying communication delays. By the construction of a suitable Lyapunov–Krasovskii functional and the utilization of the reciprocally convex approach, novel delay-dependent consensus stability and stabilization conditions for the systems are established in terms of linear matrix inequalities (LMIs), which can be easily solved by various effective optimization algorithms. One illustrative example is given to illustrate the effectiveness of the proposed methods.

Keywords: multi-teleoperator systems interval time-varying delay leader–following consensus problem Lyapunov method

Received: 14 January 2013
Revised: 13 February 2013
Accepted manuscript online:

PACS:	05.65.+b	(Self-organized systems)
	02.10.Yn	(Matrix theory)

Fund: Project supported by MEST & DGIST (12-IT-04, Development of the Medical & IT Convergence System) and the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant Nos. 2011-0009273 and 2012-0000479).

Corresponding Authors: O. M. Kwon
E-mail: madwind@chungbuk.ac.kr

Cite this article:

M. J. Park, S. M. Lee, J. W. Son, O. M. Kwon, E. J. Cha Leader–following consensus control for networked multi-teleoperator systems with interval time-varying communication delays 2013 Chin. Phys. B 22 070506

[1]	Saber R O, Fax J A and Murray R M 2007 Proc. IEEE 95 215
[2]	Jadbabie A, Lin J and Morse A S 2003 IEEE Trans. Autom. Control 48 988
[3]	DeLellis P, DiBernardo M, Garofalo F and Liuzza D 2010 Appl. Math. Comput. 217 988
[4]	Lee D and Spong M W 2007 IEEE Trans. Autom. Control 52 1469
[5]	Zhai G, Okuno S, Imae J and Kobayashi T 2011 J. Intell. Robot Syst. 63 309
[6]	Kim H, Shim H and Seo J H 2011 IEEE Trans. Autom. Control 56 200
[7]	Yan J, Guan X P and Luo X Y 2011 Chin. Phys. B 20 048901
[8]	Sun W and Dou L H 2010 Chin. Phys. B 19 120513
[9]	Shang Y L 2010 Chin. Phys. B 19 120506
[10]	Park M J, Kwon O M, Park Ju H, Lee S M and Cha E J 2012 Chin. Phys. B 21 110508
[11]	Li J Z 2011 Chin. Phys. B 20 020512
[12]	Shi Y J, Yang T, Wang W and Jin Y H 2011 Chin. Phys. B 20 020511
[13]	Ryu J H, Artigas J and Preusche C 2010 Mechatronics 20 812
[14]	Chopra N, Spong M W and Lozano R 2008 Automatica 44 2142
[15]	Lee D and Spong M W 2006 IEEE Trans. Robot. 22 269
[16]	Forouzantabar A, Talebi H A and Sedigh A K 2012 Nonlinear Dyn. 67 1123
[17]	Aziminejad A, Tavakoli M, Patel R V and Moallem M 2008 IEEE Trans. Control Syst. Technol. 16 548
[18]	Balasubramaniam P and Nagamani G 2010 Nonlinear Anal. Hybrid Systems 4 853
[19]	Balasubramaniam P, Krishnasamy R and Rakkiyappan R 2011 Nonlinear Anal. Hybrid Systems 5 681
[20]	Fridman E and Shaked U 2003 Int. J. Control 76 48
[21]	Ariba Y and Gouaisbaut F 2009 Int. J. Control 82 1616
[22]	Park M J, Kwon O M, Park J H, Lee S M and Cha E J 2012 J. Frankl. Inst. 349 1699
[23]	Ahn C K 2010 Nonlinear Anal. Hybrid Systems 4 16
[24]	Li C, Sun J and Sun R 2010 J. Fankl. Inst. 347 1186
[25]	Yang D S, Liu Z W, Zhao Y and Liu Z B 2012 Chin. Phys. B 21 040503
[26]	Slawiński E, Postigo J F and Mut V 2007 Robot. Auton. Syst. 55 205
[27]	Yang T C, Peng C, Yue D and Fei M R 2010 IET Control Theory Appl. 4 1109
[28]	Xu S and Lam J 2008 Int. J. Syst. Sci. 39 1095
[29]	Park P, Ko J W and Jeong C K 2011 Automatica. 47 235
[30]	Boyd S, Ghaoui L El, Feron E and Balakrishnan V 1994 Linear Matrix Inequalities in System and Control Theory (Philadelphia: SIAM)
[31]	Godsil C and Royle G 2001 Algebraic Graph Theory (New York: Springer-Verlag)
[32]	Graham A 1982 Kronecker Products and Matrix Calculus: with Applications (New York: John Wiley & Sons, Inc.)
[33]	Gu K 2000 Proceedings of the 39th IEEE Conference on Decision and Control, December 12-15, 2000 Sydney, Australia, pp. 2805-2810
[34]	de Oliveira M C and Skelton R E 2001 Stability Tests for Constrained Linear Systems (Berlin: Springer-Verlag)
[35]	Kim S H, Park P and Jeong C K 2010 IET Control Theory Appl. 4 1828
[36]	Gahinet P, Nemirovskii A, Laub A and Chilali M 1995 LMI Control Toolbox (Natick: The Mathworks, Inc.)

[1]	Robust H_∞ control for uncertain Markovian jump systems with mixed delays R Saravanakumar, M Syed Ali. Chin. Phys. B, 2016, 25(7): 070201.
[2]	Robust H_∞ control of uncertain systems with two additive time-varying delays M. Syed Ali, R. Saravanakumar. Chin. Phys. B, 2015, 24(9): 090202.
[3]	Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays M. Syed Ali, R. Saravanakumar. Chin. Phys. B, 2014, 23(12): 120201.
[4]	H_∞ synchronization of chaotic neural networks with time-varying delays O. M. Kwon, M. J. Park, Ju H. Park, S. M. Lee, E. J. Cha. Chin. Phys. B, 2013, 22(11): 110504.
[5]	Leader–following consensus criteria for multi-agent systems with time-varying delays and switching interconnection topologies M. J. Park, O. M. Kwon, Ju H. Park, S. M. Lee, E. J. Cha. Chin. Phys. B, 2012, 21(11): 110508.
[6]	New results on stability criteria for neural networks with time-varying delays O.M. Kwon, J.W. Kwon, and S.H. Kim. Chin. Phys. B, 2011, 20(5): 050505.
[7]	Novel delay-dependent stability criteria for neural networks with interval time-varying delay Wang Jian-An(王健安) . Chin. Phys. B, 2011, 20(12): 120701.
[8]	Synchronization criteria for coupled Hopfield neural networks with time-varying delays M.J. Park, O.M. Kwon, Ju H. Park, S.M. Lee, and E.J. Cha . Chin. Phys. B, 2011, 20(11): 110504.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Leader–following consensus control for networked multi-teleoperator systems with interval time-varying communication delays

Cite this article:

Online attention