Global stabilization of complex networks with digraph topologies via a local pinning algorithm

Automatica

Volumn 46, Issue 1, 2010, Pages 116-121

  Lu, Wenlian ^a   Li, Xiang ^a   Rong, Zhihai ^b  

^a FUDAN UNIVERSITY   (China)

^b DONGHUA UNIVERSITY   (China)

Author keywords

Chaos control; Complex network; Directed graph; Pinning control; Shortest path; Stabilizability

Indexed keywords

CHAOS CONTROL; COMPLEX NETWORKS; DIRECTED GRAPHS; PINNING CONTROL; SHORTEST PATH; STABILIZABILITY;

ALGORITHMS; CHAOTIC SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; GRAPH THEORY; SYSTEM STABILITY;

CONTROL SYSTEM STABILITY;

EID: 73049095891     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2009.10.006     Document Type: Article

References (22)

1. Barabási A.L., and Albert R. Emergence of scaling in random networks. Science 286 (1999) 509-512
2. Berman A. Completely positive matrices (2003), World Scientific Publishing, New Jersey
3. Boyd S., et al. Linear matrix inequalities in system and control theory (1994), SIAM, Philadelphia
4. Brualdi R.A., and Ryser H.J. Combinatorial matrix theory (1991), Cambridge University Press, Cambridge
5. Chen T.P., Liu X.W., and Lu W.L. Pinning complex networks by a single controller. IEEE Transactions on Circuits and Systems -I: Regular Papers 54 6 (2007) 1317-1326
6. Dashkovskiy S., Ruffer B.S., and Wirth F.R. An ISS small gain theorem for general networks. Mathematics Control, Signals and Systems 19 (2007) 93-122
7. Erdös P., and Rényi R. On random graphs. Publications Mathematics 6 (1959) 290-297
8. Godsil C., and Royle G. Algebraic graph theory (2001), Springer-Verlag, New York
9. Hu G., and Qu Z.L. Controlling spatiotemporal chaos in coupled map lattice systems. Physical Review Letters 72 (1994) 68-71
10. Jiang Z.P., and Wang Y. A generalization of the nonlinear small-gain theorem for large-scale complex systems. Proceeding of the 7th World congress on intelligent control and automation (2008) 1188-1193
11. Jungnickel D. Graphs, networks, and algorithms (2005), Springer-Verlag, Berlin Heidelberg
12. Li X., Wang X.F., and Chen G. Pinning a complex dynamical network to its equilibrium. IEEE Transactions on Circuits and Systems-I: Regular Paper 51 10 (2004) 2074-2087
13. Porfiri M., and di Bernardo M. Criteria for global pinning-controllability of complex networks. Automatica 44 (2008) 3100-3106
14. Roy R., Murphy Jr. T.W., Maier T.D., and Gills Z. Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system. Physical Review Letters 68 (1992) 1259-1262
15. Siljak D.D. Decentralized control of complex systems (1991), Academic Press, New York
16. Sorrentino F., di Bernardo M., Garofalo F., and Chen G. Controllability of complex networks via pinning. Physical Review E 75 (2007) 046103
17. Wang X.F., and Chen G. Pinning control of scale-free dynamical networks. Physics A 310 (2002) 521-531
18. Wang W., and Slotine J.J.E. A theoretical study of different leader roles in networks. IEEE Transactions on Automatic Control 51 7 (2006) 1156-1161
19. Watts D.J., and Strogatz S.H. Collective dynamics of 'small-world' networks. Nature 393 (1998) 440-442
20. Wu C.W. On bounds of extremal eigenvalues of irreducible and m-reducible matrices. Linear Algebra and Its Applications 402 (2005) 29-45
21. Xiang J., and Chen G. On the V-stability of complex dynamical networks. Automatica 43 (2007) 1049-1057
22. Yu W., Chen G., and Lü J. On pinning synchronization of complex dynamical networks. Automatica 45 (2009) 429-435