Advertisement

Observability of Nonlinear Control Systems on Time Scales - Sufficient Conditions

  • Ewa Pawłuszewicz

Summary

In the paper the problem of observability of nonlinear control systems defined on time scales is studied. For this purpose it is introduced a family of operators which in the continuous-time case coincides with Lie derivatives associated to the given system. Then it is shown that set of functions generated by this operator distinguishes states that are distinguishable. The proved sufficient condition for observability is classical, but it works not only for continuous-time case but also for the other models of time.

Keywords

time scale indistinguishability relation observability sets observability rank condition on time scales 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bohner M, Peterson A (2001) Dynamic Equations on Time Scales. Birkhauser, Boston Basel Berlin.zbMATHGoogle Scholar
  2. 2.
    Kalman RE, Falb PL, Arbib MA (1969) Topics in Mathematical System Theory. McGraw-Hill, New York.zbMATHGoogle Scholar
  3. 3.
    Sontag E. (1990) Mathematical Control Theory. Springer-Verlag, Berlin Heidelberg New York.zbMATHGoogle Scholar
  4. 4.
    Agarwal RP, Bohner M (1999) Basic calculus on time scales and some its applications. Results Math 35(1–2):3–22.zbMATHMathSciNetGoogle Scholar
  5. 5.
    Bartosiewicz Z, Pawluszewicz E (2006) Realizations of linear control systems on time scales. Control and Cybernetics 35:769–786.zbMATHMathSciNetGoogle Scholar
  6. 6.
    Fausett LV, Murty KN (2004) Controllability, Observability and Realizability Criteria on Time Scale Dynamical Systems. Nonlinear Studies 11:627–638.zbMATHMathSciNetGoogle Scholar
  7. 7.
    . Herman R., Krener AJ (1977) Nonlinear controllability and observability. IEEE Trans. Aut. Contr. 728–740.Google Scholar
  8. 8.
    Hilger S. (1990) Analysis on measure chains - a unified appproach to continuous and discrete calculus. Results Math. 18:18–56.zbMATHMathSciNetGoogle Scholar
  9. 9.
    Hilscher R., Zeidan V (2004) Calculus of variations on time scales: weak local piecewise Crd solutions with variable endpoints. J. Math. Anal. Appl. 289: 143–166.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Goodwin GC, Middleton RH, Poor HV (1992) High-Speed Digital Signal Processing and Control. Proceedings of the IEEE 80:240–259.CrossRefGoogle Scholar
  11. 11.
    . Yantir A (2003) Derivative and integration on time scale with Mathematica. Proceedings of the 5th International Mathematica Symposium: Challenging the Boundaries of Symbolic Computation 325–331.Google Scholar
  12. 12.
    . Hilger S (1988) Ein Maßkettenkalkülmit Anwendung auf Zentrumsmannig faltigkeiten. Ph.D. Thesis, Universität Würzburg.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ewa Pawłuszewicz
    • 1
  1. 1.Faculty of Computer SciencesBiałystok Technical UniversityBiałystokPoland

Personalised recommendations