Skip to main content
SpringerLink
Log in
Book cover

Positive Systems pp 205–215Cite as

Stability Analysis and Synthesis for Linear Positive Systems with Time-Varying Delays

  • Conference paper

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 389))

Abstract

This paper provides necessary and sufficient conditions for the asymptotic stability of linear positive systems subject to time-varying delays. It introduces and initiates an original method for solving directly the proposed stability and stabilization problems without using the well-known Lyapunov theory that is commonly used in the field of stability analysis. In that way and for readers convenience, the paper avoids possible long and tedious superfluous calculus.

This is a preview of subscription content, 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   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ait Rami, M., Tadeo, F.: Controller Synthesis for Linear Systems to Impose Positiveness in Closed-Loop States. In: Proceedings of the IFAC World Congress, Prague (2005)

    Google Scholar 

  2. Ait Rami, M., Tadeo, F.: Positive observation for positive discrete linear systems. In: IEEE CDC (2006)

    Google Scholar 

  3. Ait Rami, M., Tadeo, F.: Linear programming approach to impose positiveness in closed-loop and estimated states. In: Proceedings Sixteenth International Symposium on Mathematical Theory of Networks and Systems, Kyoto, Japan (2006)

    Google Scholar 

  4. Ait Rami, M., Tadeo, F.: Controller Synthesis for Positive Linear Systems with Bounded controls. IEEE Trans. on Circuits and Sys. II 54, 151–155 (2007)

    Article  Google Scholar 

  5. Ait Rami, M., Cheng, C.H., de Prada, C.: Tight robust interval observers: an LP approach. In: IEEE CDC (2008)

    Google Scholar 

  6. Ait Rami, M., Helmke, U., Tadeo, F.: Positive observation problem for time-delays linear positive systems. In: Proceedings of the 15th IEEE Med. conf., Athens (2007)

    Google Scholar 

  7. Ait Rami, M., Helmke, U., Tadeo, F.: Positive observation problem for linear time-lag positive systems. In: The 3rd IFAC Symposium on System, Structure & Control, Foz do Iguau, Brazil (2007)

    Google Scholar 

  8. Ait Rami, M., Hmamed, A., Alfidi, M.: L 1 stability and stabilization of positive 2D contineous systems. Syst. and Control Letters (2008) (accepted)

    Google Scholar 

  9. Ait Rami, M., Tadeo, F., Benzaouia, A.: Control of constrained positive discrete systems. In: Proceedings of the American Control Conf., New York (2007)

    Google Scholar 

  10. Berman, A., Plemmon, R.J.: Nonnegative matrices in the mathematical sciences. SIAM Classics Appl. Maths (1994)

    Google Scholar 

  11. Berman, A., Neumann, M., Stern, R.J.: Nonnegative Matrices in Dynamic Systems. Wiley, New York (1989)

    MATH  Google Scholar 

  12. Farina, L., Rinaldi, S.: Positive Linear Systems: Theory and Applications. Wiley, New York (2000)

    MATH  Google Scholar 

  13. Haddad, W.M., Chellaboina, V.: Stability theory for nonegative and compartmental dynamical systems with time delay. Syst. and Control Letters 51, 355–361 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Hale, J.K.: Theory of Functional Differential Equations. Springer, New York (1977)

    MATH  Google Scholar 

  15. Hmamed, A., Ait Rami, M., Afidi, M.: Controller synthesis for positive 2D systems described by the Roesser model. In: IEEE CDC (2008)

    Google Scholar 

  16. Hmamed, A., Benzaouia, A., Ait Rami, M., Tadeo, F.: Positive stabilization of discrete-time systems with unknown delay and bounded controls. In: European Control Conference, Kos, Greece (2007)

    Google Scholar 

  17. Hmamed, A., Benzaouia, A., Ait Rami, M., Tadeo, F.: Memoryless control to drive states of delayed continuous-time systems within the nonnegative orthant. In: Proceedings of the 17th World Congress, Seoul, Korea (2008)

    Google Scholar 

  18. Horn, R., Johnson, C.: Topics in Matrix Analysis. Cambridge Univ. Press, Cambridge (1991)

    MATH  Google Scholar 

  19. Kaczorek, T.: Positive 1D and 2D Systems. Springer, UK (2001)

    Google Scholar 

  20. Lewis, R.M., Anderson, B.D.O.: Insensitivity of a class of Nonlinear Compartmental Systems to the Introduction of Arbitrary Time Delays. IEEE Trans. on Circuit and Sys. 27, 604–612 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  21. Lewis, R.M., Anderson, B.D.O.: Necessary and Sufficient Condition for Delay-Independent Stability of Linear Autonomous Systems. IEEE Trans. Aut. Contr. 25, 735–739 (1980)

    Article  MATH  Google Scholar 

  22. Luenberger, D.G.: Introduction to Dynamic Systems. Wiley, New York (1979)

    MATH  Google Scholar 

  23. Ohta, Y.: Stability Criteria for Off-Diagonally Monotone Nonlinear Dynamical Systems. IEEE Trans. on Circuit and Sys. 27, 956–962 (1980)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. Ingenieria de Sistemas y Automatica, Universidad de Valladolid, 47005, Valladolid, Spain

    Mustapha Ait Rami

Authors
  1. Mustapha Ait Rami
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Instituto Universitario de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Camí de Vera s/n, 46022, Valencia, Spain

    Rafael Bru  & Sergio Romero-Vivó  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ait Rami, M. (2009). Stability Analysis and Synthesis for Linear Positive Systems with Time-Varying Delays. In: Bru, R., Romero-Vivó, S. (eds) Positive Systems. Lecture Notes in Control and Information Sciences, vol 389. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02894-6_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02894-6_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02893-9

  • Online ISBN: 978-3-642-02894-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation