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New criteria for synchronization stability of general complex dynamical networks with coupling delays. (English) Zbl 1236.34069
Summary: Complex dynamical networks are attracting more and more attention due to their ubiquity in the natural world. This Letter presents several new delay-dependent conditions for a general complex dynamical network model with coupling delays, which guarantee the synchronized states to be asymptotically stable. These conditions are expressed as linear matrix inequalities, readily solvable by available numerical software. Both continuous- and discrete-time networks are taken into consideration. It is shown theoretically that the condition for continuous-time delayed networks developed in this Letter encompasses an established result in the literature as a special case. In addition, similar delay-dependent results are derived for discrete-time delayed networks, for the first time in the literature. The most important feature of the results obtained in this Letter is that they are less conservative, which is illustrated by a numerical example.

93D99Stability of control systems
LMI toolbox
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[1] Albert, R.; Barabasi, A. -L.: Rev. mod. Phys.. 74, 47 (2002)
[2] Amaral, L. A. N.; Ottino, J. M.: Eur. phys. J. B. 38, 147 (2004)
[3] Nakamura, I.: Phys. rev. E. 68, 045104 (2003)
[4] Paul, G.; Tanizawa, T.; Havlin, S.; Stanley, H. E.: Eur. phys. J. B. 38, 187 (2004)
[5] Strogatz, S. H.: Nature. 410, 268 (2001)
[6] Wang, X. F.; Chen, G.: IEEE circuits systems mag.. 3, 6 (2003)
[7] Erdös, P.; Renyi, A.: Publ. math. Inst. hung. Acad. sci.. 5, 17 (1959)
[8] Watts, D. J.; Strogatz, S. H.: Nature. 393, 440 (1998)
[9] Barabasi, A. -L.; Albert, R.: Science. 286, 509 (1999)
[10] Barabasi, A. -L.; Albert, R.; Jeong, H.: Physica A. 272, 173 (1999)
[11] Aldana, M.: Physica D. 185, 45 (2003)
[12] Dangalchev, C.: Physica A. 338, 659 (2004)
[13] Wang, X. F.; Chen, G.: Physica A. 310, 521 (2002)
[14] Wang, X. F.; Chen, G.: IEEE trans. Circuits systems I. 49, 54 (2002)
[15] Wang, X. F.; Chen, G.: Int. J. Bifur. chaos. 12, 187 (2002)
[16] Li, C. G.; Chen, G.: Physica A. 343, 263 (2004)
[17] Kolmanovskii, V.; Myshkis, A.: Introduction to the theory and applications of functional differential equations. (1999) · Zbl 0917.34001
[18] Cao, J. D.: Phys. lett. A. 261, 303 (1999)
[19] Cao, J. D.: Phys. lett. A. 307, 136 (2003)
[20] Cao, J. D.; Li, P.; Wang, W. W.: Phys. lett. A. 353, 318 (2006)
[21] He, Y.; Wang, Q.; Zheng, W.: Chaos solitons fractals. 26, No. 5, 1349 (2005)
[22] He, Y.; Wu, M.; She, J. H.; Liu, G. P.: Systems control lett.. 51, No. 1, 57 (2004)
[23] Ho, D. W. C.; Li, J. M.; Niu, Y. G.: IEEE trans. Neural networks. 16, 625 (2005)
[24] Hua, C. C.; Guan, X. P.: Phys. lett. A. 314, 72 (2003)
[25] Hua, C. C.; Long, C. N.; Guan, X. P.: Phys. lett. A. 352, 335 (2006)
[26] Liang, J. L.; Cao, J. D.; Ho, D.: Phys. lett. A. 335, 226 (2005)
[27] Wang, Z.; Liu, Y. R.; Liu, X. H.: Phys. lett. A. 345, 299 (2005)
[28] Xu, S.; Chu, Y. M.; Lu, J. W.: Phys. lett. A. 352, 371 (2006)
[29] Gahinet, P.; Nemirovskii, A.; Laub, A. J.; Chilali, M.: LMI control toolbox user’s guide. (1995)
[30] Gahinet, P.; Apkarian, P.: Int. J. Robust nonlinear control. 4, 421 (1994) · Zbl 0808.93024
[31] Iwasaki, T.; Skelton, R. E.: Automatica. 30, No. 8, 1307 (1994)
[32] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in systems and control theory. (1994) · Zbl 0816.93004