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Warianty tytułu
Języki publikacji
Abstrakty
The formula for the solution to linear q-difference fractional-order control systems with finite memory is derived. New definitions of observability and controllability are proposed by using the concept of extended initial conditions. The rank condition for observability is established and the control law is stated.
Czasopismo
Rocznik
Tom
Strony
69--73
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
Bibliografia
- 1. Atici F. M., Eloe P. W. (2007), Fractional q-calculus on a time scale, Journal of Nonlinear Mathematical Physics, Vol.14, No 3, 333-344.
- 2. Atici F. M., Eloe P.W. (2009), Initial value problems in discrete fractional calculus, Proc. AMS, No. 13, 7981-989.
- 3. Guermah S., Djennoune S., Bettayeb M. (2008), Controllability and the observability of linear discrete-time fractional-order systems, Int. J. Appl. Math. Comput. Sci., Vol. 18, No 2, 213-222.
- 4. Jackson H. F. (1910), q-Difference equations, Am. J. Math., No 32, 305-314.
- 5. Kac V., Cheung P. (2001), Quantum calculus, New York Berlin Heidelberg.
- 6. Kaczorek T. (2007), Reachability and controllability to zero of positive fractional discrete--time systems, Proceedings of European Control Conference ECC’07, Kos, Greece.
- 7. Kaczorek T. (2008), Reachability of fractional positive continuous--time linear systems and their reachability, Int. J. Appl. Math. Comput. Sci, Vol. 18, No 2, 223-228.
- 8. Lorenzo C. F., Hartley T. T. (2009), On self-consistent operators with application to operators of fractional order, Proceedings of the ASME 2009 International Design Engineering technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2009, San Diego, California, USA.
- 9. Mozyrska D., Bartosiewicz Z. (2010), On observability concepts for nonlinear discrete--time fractional order control systems, New Trends in Nanotechnology and Fractional Calculus Applications, 305-312.
- 10. Mozyrska D., Pawłuszewicz E. (2010), Observability of linear q-difference fractional-order systems with finite initial memory, Bull. Pol. Acad. Sci. Tech. Sci., Vol. 58, No 4, 601-605.
- 11. Ortigueira M. D. (2008), The fractional quantum derivative and the generalised Euler-Cauchy equation, J. Inequal. Appl. 956-962.
- 12. Ortigueira M. D., Coito F. J. (2007), Revisiting the Initial Conditions Problem in Fractional Linear Systems, Symposium on Applied Fractional Calculus SAFC07, University of Extremadura, Badajoz, Spain.
- 13. Sierociuk D., Dzieliński A. (2006), Fractional Kalman filter algorithn for the states, parameters and order of fractonal system estimation, Int. J. Appl. Math. Comput. Sci., Vol. 16, No 1, 129-140.
- 14. Sontag E. (1990), Mathematical Control Theory, Springer – Verlag.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB2-0051-0021