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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 810625, 9 pages
http://dx.doi.org/10.1155/2013/810625
Research Article

Local Observability of Systems on Time Scales

Faculty of Computer Science, Bialystok University of Technology, Wiejska 45a, 15-351 Bialystok, Poland

Received 9 August 2013; Revised 10 October 2013; Accepted 10 October 2013

Academic Editor: Delfim F. M. Torres

Copyright © 2013 Zbigniew Bartosiewicz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. Hermann and A. J. Krener, “Nonlinear controllability and observability,” IEEE Transactions on Automatic Control, vol. 22, no. 5, pp. 728–740, 1977. View at Zentralblatt MATH · View at MathSciNet
  2. Z. Bartosiewicz, “Local observability of nonlinear systems,” Systems & Control Letters, vol. 25, no. 4, pp. 295–298, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Z. Bartosiewicz, “Real analytic geometry and local observability,” in Differential Geometry and Control (Boulder, CO, 1997), G. Ferreyra, R. Gardner, H. Hermes, and H. Sussmann, Eds., vol. 64 of Proc. Sympos. Pure Math., pp. 65–72, American Mathematical Society, Providence, RI, USA, 1999. View at Zentralblatt MATH · View at MathSciNet
  4. F. Albertini and D. D'Alessandro, “Observability and forward-backward observability of discrete-time nonlinear systems,” Mathematics of Control, Signals, and Systems, vol. 15, no. 4, pp. 275–290, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. D. Mozyrska and Z. Bartosiewicz, “Algebraic criteria for stable local ob- servability of analytic systems on n,” in Proceedings of European Control Conference (ECC '97), Brussels, Belgium, July 1997.
  6. Z. Bartosiewicz, “Observability of linear positive systems on time scales,” in Proceedings of the 51st IEEE Conference on Decision and Control, pp. 2581–2586, Maui, Hawaii, December 2012.
  7. Z. Bartosiewicz and E. Pawluszewicz, “Realizations of nonlinear control systems on time scales,” IEEE Transactions on Automatic Control, vol. 53, no. 2, pp. 571–575, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  8. E. Pawłuszewicz, “Observability of nonlinear control systems on time scales,” International Journal of Systems Science, vol. 43, no. 12, pp. 2268–2274, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  9. H. J. Sussmann, “Existence and uniqueness of minimal realizations of nonlinear systems,” Mathematical Systems Theory, vol. 10, no. 3, pp. 263–284, 1976/77. View at MathSciNet
  10. Z. Bartosiewicz and J. Johnson, “Systems on universe spaces,” Acta Applicandae Mathematicae, vol. 37, no. 3, pp. 233–266, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. R. Narasimhan, Introduction to the Theory of Analytic Spaces, Lecture Notes in Mathematics, no. 25, Springer, Berlin, Germany, 1966. View at MathSciNet
  12. H. Cartan, “Variétés analytiques réelles et variétés analytiques complexes,” Bulletin de la Société Mathématique de France, vol. 85, pp. 77–99, 1957. View at Zentralblatt MATH · View at MathSciNet
  13. G. Sh. Guseinov, “Integration on time scales,” Journal of Mathematical Analysis and Applications, vol. 285, no. 1, pp. 107–127, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. R. C. Gunning and H. Rossi, Analytic Functions of Several Complex Variables, Prentice-Hall, Englewood Cliffs, NJ, USA, 1965. View at MathSciNet
  15. F. Guaraldo, P. Macrì, and A. Tancredi, Topics on Real Analytic Spaces, Advanced Lectures in Mathematics, Friedr. Vieweg & Sohn, Braunschweig, Germany, 1986. View at MathSciNet
  16. J.-J. Risler, “Le théorème des zéros en géométries algébrique et analytique réelles,” Bulletin de la Société Mathématique de France, vol. 104, no. 2, pp. 113–127, 1976. View at Zentralblatt MATH · View at MathSciNet