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Passivity-based control and synchronization of general complex dynamical networks. (English) Zbl 1175.93208
Summary: This paper presents some sufficient conditions for complex dynamical networks with and without coupling delays in the state to be passive. Based on the passivity property and linearization, control and synchronization of the dynamical networks are also addressed. An example and simulation results are included.

MSC:
93D99Stability of control systems
93B18Linearizability of systems
93C10Nonlinear control systems
93C15Control systems governed by ODE
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[1] Angeli, D., & Bliman, P.-A. (2005). Extension of a result by Moreau on stability of leaderless multi-agent systems. In Proc. 44th IEEE Conf. on decision and control & European control conference (pp. 759-764)
[2] Albert, R.; Jeong, H.; Barabási, A. -L.: Diameter of the world wide web, Nature 401, 130-131 (1999)
[3] Albert, R.; Jeong, H.; Barabási, A. -L.: Error and attack tolerance of complex networks, Nature 406, 378-382 (2000)
[4] Arcak, M. (2006). Passivity as a design tool for group coordination. In Proc. 2006 American control conference
[5] Barabási, A. L.; Albert, R.: Emergence of scaling in random networks, Science 285 (1999) · Zbl 1226.05223
[6] Barabási, A. L.; Albert, R.; Jeong, H.; Bianconi, G.: Power-law distribution of the world wide web, Science 287, 2115a (2000)
[7] Belykh, V. N.; Belykh, I. V.; Hasler, M.: Connection graph stability method for synchronized coupled chaotic systems, Physica D 195, 159-187 (2004) · Zbl 1098.82622 · doi:10.1016/j.physd.2004.03.012
[8] Belykh, I. V.; Belykh, V. N.; Hasler, M.: Blinking model and synchronization in small-world networks with a time-varying coupling, Physica D 195, 188-206 (2004) · Zbl 1098.82621 · doi:10.1016/j.physd.2004.03.013
[9] Barajas-Ramírez, J. -G.; Chen, G.; Shieh, L. S.: Hybrid chaos synchronization, International journal of bifurcation and chaos 13, 1197-1216 (2003) · Zbl 1129.93493 · doi:10.1142/S021812740300714X
[10] Brogliato, B.; Lozano, R.; Maschke, B.; Egeland, O.: Dissipative systems analysis and control, (2007) · Zbl 1121.93002
[11] Chen, G.; Dong, X.: From chaos to order: methodologies, perspectives, and applications, (1998) · Zbl 0908.93005
[12] Chua, L. O.; Komuro, M.; Matsumoto, T.: The double scroll family, part I: Rigorous proof of chaos, IEEE transactions on circuits and systems (I) 33, 1073-1097 (1986)
[13] Cao, J.; Lu, J.: Adaptive synchronization of neural networks with or without time-varying delay, Chaos 16, 013133 (2006) · Zbl 1144.37331 · doi:10.1063/1.2178448
[14] Cao, J.; Li, P.; Wang, W.: Global synchronization in arrays of delayed neural networks with constant and delayed coupling, Physics letters A 353, 318-325 (2006)
[15] Chen, G.; Yu, X.: Chaos control: theory and applications, (2003) · Zbl 1029.00015
[16] Earl, M. G.; Strogatz, S. H.: Synchronization in oscillator networks with delayed coupling: A stability criterion, Physical review E 67, 036204 (2003)
[17] Faloutsos, M.; Faloutsos, P.; Faloutsos, C.: On power-law relationships of the Internet topology, Computer communication review 29, 251-263 (1999) · Zbl 0889.68050
[18] Guo, S. M.; Shieh, L. S.; Chen, G.; Lin, C. -F.: Effective chaotic orbit tracker: A prediction-based digital redesign approach, IEEE transactions on circuits and systems (I) 47, 1557-1570 (2000) · Zbl 0999.93024 · doi:10.1109/81.895324
[19] Guo, S. M.; Shieh, L. S.; Chen, G.; Ortega, M.: Ordering chaos in Chua’s circuit: A sampled-data feedback and digital redesign approach, International journal of bifurcation and chaos 10, 2221-2231 (2000) · Zbl 0956.93505 · doi:10.1142/S0218127400001389
[20] Huang, X.; Cao, J.: Generalized synchronization for delayed chaotic neural networks: A novel coupling scheme, Nonlinearity 19, 2797-2811 (2006) · Zbl 1111.37022 · doi:10.1088/0951-7715/19/12/004
[21] Ihle, I. F., Arcak, M., & Fossen, T. I. (2006). Passivity-based designs for synchronized path following. In Proc. 45th IEEE conf. on decision and control (pp. 4319-4326) · Zbl 1128.93331
[22] Khalil, H. K.: Nonlinear systems, (2002) · Zbl 1003.34002
[23] Li, C.; Chen, G.: Local stability and Hopf bifurcation in small-world delayed networks, Chaos, solitons and fractals 20, 353-361 (2004) · Zbl 1045.34047 · doi:10.1016/S0960-0779(03)00405-3
[24] Li, C.; Chen, G.: Synchronization in general complex dynamical networks with coupling delays, Physica A 343, 263-278 (2004)
[25] Li, C.; Li, S.; Liao, X.; Yu, J.: Synchronization in coupled map lattices with small-world delayed interactions, Physica A 335, 365-370 (2004)
[26] Lee, D. J., & Spong, M.W. (2006). Agreement with non-uniform information delays. In Proc. 2006 American control conference (pp. 756-761)
[27] Li, C.; Xu, H.; Liao, X.; Yu, J.: Synchronization in small-world oscillator networks with coupling delays, Physica A 335, 359-364 (2004)
[28] Lü, J.; Yu, X.; Chen, G.: Chaos synchronization of general complex dynamical networks, Physica A 334, 281-302 (2004)
[29] Strogatz, S. H.: Exploring complex networks, Nature 410, 268-276 (2001)
[30] Teixeira, M. C. M.; Zak, S. H.: Stabilizing controller design for uncertain nonlinear systems using fuzzy models, IEEE transactions on fuzzy systems 7, 133-142 (1999)
[31] Watts, D. J.: Small world, (1999) · Zbl 0940.82029
[32] Wang, X. F.; Chen, G.: Synchronization in small-world dynamical networks, International journal of bifurcation and chaos 12, 187-192 (2002)
[33] Wang, X. F.; Chen, G.: Synchronization in scale-free dynamical networks: robustness and fragility, IEEE transactions on circuits and systems I 49, 54-62 (2002)
[34] Watts, D. J.; Strogatz, S. H.: Collective dynamics of small-world networks, Nature 393, 440-442 (1998)
[35] Yang, X. S.: Fractals in small-world networks with time-delay, Chaos, solitons and fractals 13, 215-219 (2002) · Zbl 1019.37052 · doi:10.1016/S0960-0779(00)00265-4
[36] Yeung, M. K. S.; Strogatz, S. H.: Time delay in the Kuramoto model of coupled oscillators, Physical review letters 82, 648-651 (1999)