Skip to main content

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

Summary

The algebraic notion of zero module of a linear, dynamical system, introduced by M. Sain and B. Wyman, allows us to generalize the notion of zero to frameworks that differ from the lassical one. In particular, it is possible to define zeros for systems with coefficients in a ring and to relate such a notion to geometric concepts. On this basis, the chapter considers zeros for time-delay linear systems and it investigates their properties in connection with inversion and other control problems.

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

Access this chapter

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 EPUB and 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

References

  1. G. Basile, G. Marro, Controlled and Conditioned Invariants in Linear System Theory, Prentice-Hall, New York (1992)

    MATH  Google Scholar 

  2. J. W. Brewer, J. W. Bunce and F. S. Van Vleck, Linear Systems Over Commutative Rings, Marcel Dekker, New York (1986)

    MATH  Google Scholar 

  3. G. Conte, A. M. Perdon, An algebraic notion of zeros for systems over rings, Proc. Int. Symp.MTNS’83 (Beer Sheva - Israele, 1983), Lecture Notes in Control and Information Science, Springer-Verlag, vol. 58 (1984) pp 166–182

    Google Scholar 

  4. G. Conte, A.M. Perdon, Noninteracting control problems for delay-differential systems via systems over rings, Journal Europ‘en des Syst’mes Automatis’s, 31, (1997)

    Google Scholar 

  5. G. Conte, A.M. Perdon and A. Lombardo, Dynamic feedback decoupling problem for delay-differential systems via systems over rings, Mathematics and Computers in Simulation, 1462, (1998)

    Google Scholar 

  6. G. Conte, A.M. Perdon, The geometric approach for systems over rings, Proceedings 37th IEEE Conference on Decision and Control, Tampa, FL (1998)

    Google Scholar 

  7. G. Conte, A. M. Perdon, Disturbance decoupling with stability for delay differential systems, Proc. 38th IEEE Conference on Decision and Control, Phoenix, AZ (1999)

    Google Scholar 

  8. G. Conte, A. M. Perdon, Systems over Rings: Geometric Theory and Applications, Annual Review in Control, no. 24, (2000)

    Google Scholar 

  9. G. Conte, A. M. Perdon, Invertibility and Inversion for Systems over Rings and Applications to Delay-differential Systems, Proc. 39th IEEE Conference on Decision and Control, Sydney, Australia (2000)

    Google Scholar 

  10. G. Conte, A.M. Perdon and R. Iachini, Inversion Problems for Time-delay Systems via Systems over Rings, Proc. IFAC Symposium on System Structure and Control, Prague, Czech Republic (2001)

    Google Scholar 

  11. G. Conte, A. M. Perdon and G. Guidone-Peroli, The Fundamental Problem of Residual Generation for Linear Time Delay Systems, Proc. IFAC Workshop on Linear Time Delay Systems LTDS03, Paris, France (2003)

    Google Scholar 

  12. G. Conte, A. M. Perdon and G. Guidone-Peroli, Unknown Input Observer for Linear Delay Systems: a Geometric Approach, Proc. 42th IEEE Conference on Decision and Control, Maui, Hawaii (2003)

    Google Scholar 

  13. G. Conte, A.M. Perdon, Unknown Input Observer and Residual Generators for Linear Time Delay Systems, in “Current Trends in Nonlinear Systems and Control”, L. Menini, L. Zaccarian, and C.T. Abdallah Eds, Birkhauser, Boston, MA (2005)

    Google Scholar 

  14. G. Conte, A.M. Perdon, Modeling Time-delay Systems by Means of Systems with Coefficients in a Ring, Proc. Workshop on Modeling and Control of Complex Systems, Ayia Napa, Cyprus (2005)

    Google Scholar 

  15. G. Conte, A.M. Perdon and C.H. Moog, Inversion and Tracking Problems for Time Delay Linear Systems, in “Applications of Time-Delay Systems” , LNCIS 352, J. Chiasson and J.J. Loiseau Eds., Springer-Verlag (2007) pp 267–284

    Google Scholar 

  16. B. Datta, M. L. Hautus, Decoupling of multivariable control systems over unique factorization domains, SIAM Journal on Control and Optimization, 22, 1 (1984), pp 28–39

    Article  MathSciNet  MATH  Google Scholar 

  17. M.L. Hautus, Controlled invariance in systems over rings, Springer Lecture Notes in Control and Information Science, vol. 39 (1982)

    Google Scholar 

  18. A.M. Perdon, G. Guidone-Peroli and M. Caboara, Algorithms for geometric control of systems over rings, Proc. 2nd IFAC Conference Control Systems (CSD’03), Bratislava, Slovak Republic (2003)

    Google Scholar 

  19. A. M. Perdon, M. Anderlucci, Un g’en’nrateur de r’esidus pour syst’emes ’a retard, Proc. Conf’erence Internationale Francophone d’Automatique, CIFA 2006, Bordeaux, France (2006)

    Google Scholar 

  20. A.M. Perdon, M. Anderlucci and M. Caboara, Effective computations for geometric control theory, International Journal of Control, vol. 79, no. 11 (2006), pp 1401–1417

    Article  MathSciNet  MATH  Google Scholar 

  21. C. B. Schrader, M. K. Sain, Research on System Zeros: A Survey, International Journal of Control, vol. 50, (1989) pp 1407–1433

    Article  MathSciNet  MATH  Google Scholar 

  22. E.D. Sontag, Linear systems over commutative rings: A survey, Ricerche di Automatica, 7 (1976) pp 1–34

    Google Scholar 

  23. E.D. Sontag, Linear systems over commutative rings: a (partial) updated survey, Control science and technology for the progress of society, Vol. 1 (Kyoto, 1981), pages 325–330.

    Google Scholar 

  24. W. M. Wonham, Linear Multivariable Control: A Geometric Approach, 3rd Ed., Springer-Verlag, Berlin (1985)

    MATH  Google Scholar 

  25. B. Wyman, M. K. Sain, The Zero Module and Essential Inverse Systems, IEEE Trans. Circuits and Systems, CAS-28, February (1981), 112–126

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Giuseppe Conte .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Birkhäuser Boston, a part of Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Conte, G., Perdon, A.M. (2008). Zeros in Linear Time-Delay Systems. In: Won, CH., Schrader, C., Michel, A. (eds) Advances in Statistical Control, Algebraic Systems Theory, and Dynamic Systems Characteristics. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4795-7_8

Download citation

Publish with us

Policies and ethics