IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v383y2007i2p733-744.html
   My bibliography  Save this article

Stabilization of a class of dynamical complex networks based on decentralized control

Author

Listed:
  • Liu, Xian
  • Wang, Jinzhi
  • Huang, Lin

Abstract

This paper deals with a stabilization problem for a class of dynamical complex networks with each node being a general Lur’e system. Based on a Lur’e–Postnikov function and a special decentralized control strategy, the problem of designing a linear feedback controller such that states of all nodes are globally stabilized onto an expected homogeneous state is addressed. A controller design method based on parameter-dependent Lur’e–Postnikov function is proposed in order to reduce the conservativeness and the controller can be constructed via feasible solutions of a certain set of linear matrix inequalities (LMIs). A dynamical network composed of identical Chua's circuits is adopted as a numerical example to demonstrate the effectiveness of the proposed results.

Suggested Citation

  • Liu, Xian & Wang, Jinzhi & Huang, Lin, 2007. "Stabilization of a class of dynamical complex networks based on decentralized control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 733-744.
    • Handle: RePEc:eee:phsmap:v:383:y:2007:i:2:p:733-744
    DOI: 10.1016/j.physa.2007.05.030
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437107005444
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2007.05.030?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fan, Jin & Li, Xiang & Fan Wang, Xiao, 2005. "On synchronous preference of complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(2), pages 657-666.
    2. Wang, Xiao Fan & Chen, Guanrong, 2002. "Pinning control of scale-free dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 521-531.
    3. Fan, Jin & Wang, Xiao Fan, 2005. "On synchronization in scale-free dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 443-451.
    4. Michael B. Elowitz & Stanislas Leibler, 2000. "A synthetic oscillatory network of transcriptional regulators," Nature, Nature, vol. 403(6767), pages 335-338, January.
    5. Timothy S. Gardner & Charles R. Cantor & James J. Collins, 2000. "Construction of a genetic toggle switch in Escherichia coli," Nature, Nature, vol. 403(6767), pages 339-342, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gao, Zilin & Guo, Changyuan & Li, Yongfu & Liu, Lizhi & Luo, Weimin, 2023. "Stabilization of a structurally balanced complex network with similar nodes of different dimensions," Applied Mathematics and Computation, Elsevier, vol. 458(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liu, Xian & Wang, Jinzhi & Huang, Lin, 2007. "Global synchronization for a class of dynamical complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 543-556.
    2. Avraham E Mayo & Yaakov Setty & Seagull Shavit & Alon Zaslaver & Uri Alon, 2006. "Plasticity of the cis-Regulatory Input Function of a Gene," PLOS Biology, Public Library of Science, vol. 4(4), pages 1-1, March.
    3. Weiyue Ji & Handuo Shi & Haoqian Zhang & Rui Sun & Jingyi Xi & Dingqiao Wen & Jingchen Feng & Yiwei Chen & Xiao Qin & Yanrong Ma & Wenhan Luo & Linna Deng & Hanchi Lin & Ruofan Yu & Qi Ouyang, 2013. "A Formalized Design Process for Bacterial Consortia That Perform Logic Computing," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-9, February.
    4. T. Ochiai & J. C. Nacher, 2007. "Stochastic analysis of autoregulatory gene expression dynamics," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 14(4), pages 377-388, November.
    5. Thomas B. Kepler & Timothy C. Elston, 2001. "Stochasticity in Transcriptional Regulation: Origins, Consequences and Mathematical Representations," Working Papers 01-06-033, Santa Fe Institute.
    6. Luis Mier-y-Terán-Romero & Mary Silber & Vassily Hatzimanikatis, 2010. "The Origins of Time-Delay in Template Biopolymerization Processes," PLOS Computational Biology, Public Library of Science, vol. 6(4), pages 1-15, April.
    7. Tai-Yin Chiu & Hui-Ju K Chiang & Ruei-Yang Huang & Jie-Hong R Jiang & François Fages, 2015. "Synthesizing Configurable Biochemical Implementation of Linear Systems from Their Transfer Function Specifications," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-27, September.
    8. Tobias May & Lee Eccleston & Sabrina Herrmann & Hansjörg Hauser & Jorge Goncalves & Dagmar Wirth, 2008. "Bimodal and Hysteretic Expression in Mammalian Cells from a Synthetic Gene Circuit," PLOS ONE, Public Library of Science, vol. 3(6), pages 1-7, June.
    9. Evgeni V Nikolaev & Eduardo D Sontag, 2016. "Quorum-Sensing Synchronization of Synthetic Toggle Switches: A Design Based on Monotone Dynamical Systems Theory," PLOS Computational Biology, Public Library of Science, vol. 12(4), pages 1-33, April.
    10. Zomorrodi, Ali R. & Maranas, Costas D., 2014. "Coarse-grained optimization-driven design and piecewise linear modeling of synthetic genetic circuits," European Journal of Operational Research, Elsevier, vol. 237(2), pages 665-676.
    11. Goodrich, Christopher S. & Matache, Mihaela T., 2007. "The stabilizing effect of noise on the dynamics of a Boolean network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 334-356.
    12. Keun-Young Kim & Jin Wang, 2007. "Potential Energy Landscape and Robustness of a Gene Regulatory Network: Toggle Switch," PLOS Computational Biology, Public Library of Science, vol. 3(3), pages 1-13, March.
    13. Singh, Vijai & Chaudhary, Dharmendra Kumar & Mani, Indra & Dhar, Pawan Kumar, 2016. "Recent advances and challenges of the use of cyanobacteria towards the production of biofuels," Renewable and Sustainable Energy Reviews, Elsevier, vol. 60(C), pages 1-10.
    14. Samanthe M Lyons & Wenlong Xu & June Medford & Ashok Prasad, 2014. "Loads Bias Genetic and Signaling Switches in Synthetic and Natural Systems," PLOS Computational Biology, Public Library of Science, vol. 10(3), pages 1-16, March.
    15. Zhou, Peipei & Cai, Shuiming & Liu, Zengrong & Chen, Luonan & Wang, Ruiqi, 2013. "Coupling switches and oscillators as a means to shape cellular signals in biomolecular systems," Chaos, Solitons & Fractals, Elsevier, vol. 50(C), pages 115-126.
    16. Nasimul Noman & Taku Monjo & Pablo Moscato & Hitoshi Iba, 2015. "Evolving Robust Gene Regulatory Networks," PLOS ONE, Public Library of Science, vol. 10(1), pages 1-21, January.
    17. Ankit Gupta & Corentin Briat & Mustafa Khammash, 2014. "A Scalable Computational Framework for Establishing Long-Term Behavior of Stochastic Reaction Networks," PLOS Computational Biology, Public Library of Science, vol. 10(6), pages 1-16, June.
    18. Duncan Ingram & Guy-Bart Stan, 2023. "Modelling genetic stability in engineered cell populations," Nature Communications, Nature, vol. 14(1), pages 1-12, December.
    19. Lu, Wen & Zhang, Yuhao & Qian, Yu & Pandey, Vikas & Qu, Zhilin & Zhang, Zhaoyang, 2021. "Bursting and complex oscillatory patterns in a gene regulatory network model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    20. Betz, Ulrich A.K. & Arora, Loukik & Assal, Reem A. & Azevedo, Hatylas & Baldwin, Jeremy & Becker, Michael S. & Bostock, Stefan & Cheng, Vinton & Egle, Tobias & Ferrari, Nicola & Schneider-Futschik, El, 2023. "Game changers in science and technology - now and beyond," Technological Forecasting and Social Change, Elsevier, vol. 193(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:383:y:2007:i:2:p:733-744. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.