Abstract
Based on feedback control, a problem is discussed in which the state variables of nodes of general complex delayed dynamical networks are controlled to its equilibrium. The delay differential inequality is employed to investigate delay-dependent of this system and some sufficient conditions for asymptotic stability are presented. At the same time, they provide concrete bounds of the delays in terms of explicit expression. A scale-free network is discussed in numerical simulations. They show the effectiveness and feasibility of the proposed conditions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Watts, D.J., Strogatz, S.H.: Collective Dynamics of Small-world. Nature 393, 440–442 (1998)
Barabasi, A.L., Albert, R.: Emergence of Scaling in Random Networks. Science 286, 509–512 (1999)
Newman, M.E.J.: The Structure and Function of Complex Networks. SIAM Rev. 45(2), 167–256 (2003)
Wang, X.F., Li, X., Chen, G.R.: Theory and Application of the Complex Networks. Qinghua university press, Beijing (2006)
Wang, X.F., Chen, G.: Pinning Control of Scale-free Dynamical Networks. Physica A 310, 521–531 (2002)
Li, X., Wang, X.F., Chen, G.: Pinning a Complex Dynamical Network to Its Equilibrium. IEEE Trans. Circuits Syst. -I 51(10), 2074–2087 (2004)
Fan, Z.P., Chen, G.: Pinning Control of Scale-free Complex Networks. In: Proceedings of the IEEE ISCAS 2005 Kobe, Japan, pp. 284–287 (2005)
Chen, G., Fan, Z.P.: Modelling, Control and Synchronization of Complex Networks. In: Proceedings of 2005 Chinese Control and Decision Conference, pp. 22–31 (2005)
Li, X., Wang, X.F.: Feedback Control of Scal-free Coupled Henon maps. In: Proceeding of the Eighth International Conference on control, Automation, Robotics and Vision at Kumming, China, pp. 574–578 (2004)
Albert, R., Jeong, H., Barabśi, A.-L.: Error and Attack Tolerance of Complex Networks. Nature 406, 378–482 (2000)
Albert, R., Barabsi, A.L.: Statistical Mechanics of Complex Networks. Rev. Mod. Phys. 74, 47–97 (2002)
Wang, X.F.: Complex Networks: Topology, Dynamics and Synchronization. International Journal of Bifurcation & Chaos 12(5), 885–916 (2002)
Wang, X., Chen, G.: Synchronization in Scale-free Dynamical Networks: Robustness and Fragility. IEEE Trans.on Circuits and Systems 49(1), 54–62 (2002)
Zhou, J., Lu, J.A., Lu, J.H.: Adaptive Synchronization of an Uncertain Complex Dynamical Network. IEEE Transactions on Automatic Control 51(4), 652–656 (2006)
Chen, J.Y., Wong, K.W., Shuai, J.W.: Phase Synchronization in Coupled Chaotic Oscillators with Time Delay. Phys. Rev. E 66, 56–203 (2002)
Lu, W., Chen, T.: Synchronization of Coupled Connected Neural Networks with Delays. IEEE Trans. Circuits Syst. I 51, 2491–2503 (2004)
Tu, L.L., Lu, J.A.: Stability of a Model for a Delayed Genetic Regulatory Network, Dynamics of Continuous. Discrete and Impulsive Systems 13, 429–439 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tu, L. (2009). Feedback Control in General Complex Delayed Dynamical Networks. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01510-6_114
Download citation
DOI: https://doi.org/10.1007/978-3-642-01510-6_114
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01509-0
Online ISBN: 978-3-642-01510-6
eBook Packages: Computer ScienceComputer Science (R0)