Skip to main content
SpringerLink
Log in

Stability of Hybrid Systems and Related Questions from Systems Biology

  • Chapter
Advances in Control, Communication Networks, and Transportation Systems

Part of the book series: Systems and Control: Foundations & Applications ((SCFA))

  • 967 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Aaron and S. Sastry, Blowing up affine hybrid systems, In IEEE Conference on Decision and Control, 473–478, Dec. 2004.

    Google Scholar 

  2. R. Alur, C. Belta, F. Ivancic, V. Kumar, M. Mintz, G.J. Pappas, H. Rubin, and J. Schug, Hybrid modeling and simulation of biomolecular networks, In M.D. DiBenedetto and A.L. Sangiovanni-Vincentelli, Eds., Hybrid Systems: Computation and Control, LNCS 2034:19–32, Springer-Verlag, 2001.

    Google Scholar 

  3. R. Alur, C. Courcoubetis, N. Halbwachs, T.A. Henzinger, P.H. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine, The Algorithmic analysis of hybrid systems, Theoretical Computer Science, 138(1):3–34, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  4. R. Alur, C. Courcoubetis, T.A. Henzinger, and P.H. Ho, Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems, In R.L. Grossman, A. Nerode, A.P. Ravn and H. Richel, Eds., Hybrid Systems, LNCS 736:209–229, Springer-Verlag, 1993.

    Google Scholar 

  5. R. Alur, T. Dang, and F. Ivancic, Progress on reachability analysis of hybrid systems using predicate abstraction, In O. Maler and A. Pnueli, Eds., Hybrid Systems: Computation and Control, LNCS 2623:4–19, Springer-Verlag, 2003.

    Google Scholar 

  6. D. Angeli and E.D. Sontag, Monotone control systems, IEEE Transaction on Automatic Control, 48:1684–1698, 2003.

    Article  MathSciNet  Google Scholar 

  7. D. Angeli and E.D. Sontag, An analysis of a circardian model using the smallgain approach to monotone systems (I), In IEEE Conference on Decision and Control, 575–578, Dec. 2004.

    Google Scholar 

  8. N. Barkai and S. Leibler, Circadian clocks limited by noise, Nature, 403:267–268, 2000.

    Google Scholar 

  9. R.W. Brockett, Pulses, periods, and cohomological terms in functional expansions, In System Theory, Springer-Verlag, 1993.

    Google Scholar 

  10. A. Cornish-Bowden, Fundamentals of Enzyme Kinetics (3rd edition), Portland Press, 2004.

    Google Scholar 

  11. R. DeCarlo, M. Branicky, S. Pettersson, and B. Lennartson, Perspectives and results on the stability and stabilizability of hybrid systems, Proceedings of IEEE, Special Issue on Hybrid Systems, 88(7):1069–1082, 2000.

    Google Scholar 

  12. L. Van Den Dries, Tame topology and o-minimal structures, London Mathematical Society Lecture Note, 248, Cambridge University Press, 1998.

    Google Scholar 

  13. R. Ghosh, A. Tiwari, and C. Tomlin, Automated symbolic reachability analysis; with application to delta-notch signaling automata, In O. Maler and A. Pnueli, Eds., Hybrid Systems: Computation and Control (HSCC’03), LNCS 2623:233–248, Springer-Verlag, 2003.

    Google Scholar 

  14. A. Goldbeter, A Model for circadian oscillations in the drosophila period protein (PER), Proc. Royal Soc. London B Biol. Sci., 261:319–324, 1995.

    Google Scholar 

  15. J.P. Keener and J. Sneyd, Mathematical Physiology, Springer-Verlag, 1998.

    Google Scholar 

  16. M. Kourjanski and P. Varaiya, Stability of hybrid systems, In R. Alur, T.A. Henzinger, E.D. Sontag, Eds., Hybrid Systems III: Verification and Control, LNCS 1066:413–423, Springer-Verlag, 1996.

    Google Scholar 

  17. J.P. LaSalle, Stability theory for ordinary differential equations, J. Diff. Equat., 4:57–65, 1968.

    Article  MATH  MathSciNet  Google Scholar 

  18. J. Lygeros, K.H. Johansson, S.N. Simić, J. Zhang, and S. Sastry, Dynamical properties of hybrid automata, IEEE Transactions on Automatic Control, 48(1):2–14, 2003.

    Article  Google Scholar 

  19. B. Mishra, Computational Differential Algebra, 111–145, World-Scientific, Singapore, 2000.

    Google Scholar 

  20. B. Mishra, A Symbolic approach to modeling cellular behavior, In S. Sahni, V.K. Prasanna and U. Shukla, Eds., High Performance Computing, LNCS 2552:725–732, Springer-Verlag, 2002.

    Google Scholar 

  21. A. Nerode and W. Kohn, Hybrid systems and constraint logic programming, In D.S. Warren, Ed., International Conference on Logic Programming, 18–24, MIT Press, 1993.

    Google Scholar 

  22. A. Tarski, A Decision Method for Elementary Algebra and Geometry, Univ. California Press, 1951.

    Google Scholar 

  23. A. Tiwari and G. Khanna, Series of abstraction for hybrid automata, In C.J. Tomlin and M. Greenstreet, Eds., Hybrid Systems: Computation and Control, LNCS 2289:465–478, Springer-Verlag, 2002.

    Google Scholar 

  24. E.O. Voit, Computational Analysis of Biochemical Systems: A Practical Guide for Biochemists and Molecular Biologists, Cambridge University Press, 2000.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mathematics and Computer Science, University of Udine, Udine, Italy

    C. Piazza

  2. Courant Institute of Mathematical Science and School of Medicine, NYU, New York, USA

    B. Mishra

Authors
  1. C. Piazza
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Mishra
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Systems Research and Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, 20742, USA

    E. H. Abed

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Birkhäuser Boston

About this chapter

Cite this chapter

Piazza, C., Mishra, B. (2005). Stability of Hybrid Systems and Related Questions from Systems Biology. In: Abed, E.H. (eds) Advances in Control, Communication Networks, and Transportation Systems. Systems and Control: Foundations & Applications. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4409-1_3

Download citation

Publish with us

Policies and ethics

Search

Navigation