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Analysis of Synchronizing Biochemical Networks via Incremental Dissipativity

  • Abdullah Hamadeh
  • Jorge Gonçalves
  • Guy-Bart Stan
Chapter

Abstract

Synchronization, defined in a broad sense, is the phenomenon in which communicating agents coordinate outputs. The abundance of examples of this process in nature and engineering has led to its becoming an active sub-area of research in networks theory, as evidenced by the multitude of publications on the subject [4].

Keywords

Dissipativity Incremental dissipativity Passive Passivity Incremental signal Zero-state detectability Storage function Supply rate Incremental supply rate Incrementally passive Incrementally output feedback passive (iOFP) 

References

  1. 1.
    Angeli D (2002) A Lyapunov approach to incremental stability properties. IEEE Trans Autom Control 47:410–422CrossRefGoogle Scholar
  2. 2.
    Arcak M, Sontag E (2006) Diagonal stability for a class of cyclic systems and applications. Automatica 42:1531–1537CrossRefGoogle Scholar
  3. 3.
    Barker GP, Berman A, Plemmons RJ (1978) Positive diagonal solutions to the Lyapunov equations. Linear and Multilinear Algebra 5(4):249–256Google Scholar
  4. 4.
    Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU (2006) Complex networks: structure and dynamics. Phys Rep 424(4–5):175–308CrossRefGoogle Scholar
  5. 5.
    Cremean LB, Murray RM (2003) Stability analysis of interconnected nonlinear systems under matrix feedback. In: Proceedings of the 42nd Conference on Decision and Control, Maui, Hawaii, USA, vol 4, pp 3078–3083Google Scholar
  6. 6.
    Demidovich BP (1967) Lectures on stability theory. Nauka, MoscowGoogle Scholar
  7. 7.
    Dockery JD, Keener JP (2001) A mathematical model for quorum sensing in pseudomonas aeruginosa. Bull Math Biol 63(1):95–116PubMedCrossRefGoogle Scholar
  8. 8.
    Elowitz MB, Leibler S (2000) A synthetic oscillatory network of transcriptional regulators. Nature 403:335–338PubMedCrossRefGoogle Scholar
  9. 9.
    Garcia-Ojalvo J, Elowitz MB (2004) Modeling a synthetic multicellular clock: repressilators coupled by quorum sensing. Proc Nat Acad Sci 101(30):10955–10960Google Scholar
  10. 10.
    Gonze D, Bernard S, Waltermann C, Kramer A, Herzel H (2005) Spontaneous synchronization of coupled circadian oscillators. Biophys J 89:120–189Google Scholar
  11. 11.
    Hamadeh A, Stan G, Goncalves J (2008) Robust synchronization in networks of cyclic feedback systems. In: Proceedings of the 47th IEEE Conference on Decision and Control (IEEE-CDC)Google Scholar
  12. 12.
    Hamadeh AO, Stan GB, Sepulchre R, Gonçalves JM (2012) Global state synchronization in networks of cyclic feedback systems. IEEE Trans Autom Control 57:478–483CrossRefGoogle Scholar
  13. 13.
    Lohmiller W, Slotine JJE (1998) On contraction analysis for nonlinear systems. Automatica 34(6):683–696CrossRefGoogle Scholar
  14. 14.
    Olfati-Saber R, Murray RM (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Control 49(9):1520–1533CrossRefGoogle Scholar
  15. 15.
    Pavlov A, Pogromsky A, van de Wouw N, Nijmeijer H (2004) Convergent dynamics, attribute to Boris Pavlovich Demidovich. Syst Control Lett 52:257–261CrossRefGoogle Scholar
  16. 16.
    Pogromsky A, Nijmeijer H (2001) Cooperative oscillatory behavior of mutually coupled dynamical systems. IEEE Trans Circuits Syst I: Fundam Theory Appl 48(2):152–162CrossRefGoogle Scholar
  17. 17.
    Scardovi L, Arcak M, Sontag E (2009) Synchronization of interconnected systems with an input–output approach. Part I: main results. In: Proceedings of the 48th IEEE Conference on Decision and Control, pp 609–614Google Scholar
  18. 18.
    Sepulchre R, Jankovic M, Kokotovic P (1997) Constructive nonlinear control. Springer, New YorkGoogle Scholar
  19. 19.
    Sontag E (2005) Passivity gains and the “secant condition” for stability. Automatica 55:177–183Google Scholar
  20. 20.
    Sontag ED, Arcak M (2008) Lecture notes in control and information sciences. Chapter passivity-based stability of interconnection structures. Springer, Berlin/Heidelberg, pp 195–204Google Scholar
  21. 21.
    Stan GB (March 2005) Global analysis and synthesis of oscillations: a dissipativity approach. PhD thesis, University of LiegeGoogle Scholar
  22. 22.
    Stan GB, Sepulchre R (2007) Analysis of interconnected oscillators by dissipativity theory. IEEE Trans Autom Control 52:256–270CrossRefGoogle Scholar
  23. 23.
    Stan GB, Hamadeh A, Sepulchre R, Goncalves J (2007) Output synchronization in networks of cyclic biochemical oscillators. In: Proceedings of the 26th IEEE American Control Conference (IEEE-ACC)Google Scholar
  24. 24.
    Vidyasagar M (1981) Input–output analysis of large scale interconnected systems. Springer-Verlag, BerlinCrossRefGoogle Scholar
  25. 25.
    Willems J (1972) Dissipative dynamical systems: parts I and II. Arch Ration Mech Anal 45:321–393CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Abdullah Hamadeh
    • 1
  • Jorge Gonçalves
    • 2
  • Guy-Bart Stan
    • 3
  1. 1.Department of Mechanical EngineeringMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of EngineeringUniversity of CambridgeCambridgeUK
  3. 3.Department of Bioengineering Imperial CollegeCentre for Synthetic Biology and InnovationLondonUK

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