Skip to main content
SpringerLink
Log in

Reachability of Fractional Positive Continuous-Time Linear Systems with Two Different Fractional Orders

  • Conference paper
Recent Advances in Automation, Robotics and Measuring Techniques

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 267))

Abstract

The reachability problem for the fractional positive continuous-time linear systems with two different fractional orders is formulated and solved. Sufficient conditions for the reachability are established. Applications of the proposed conditions is demonstrated on example of electrical circuit.

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

Access this chapter

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. BusƂowicz, M.: Stability of linear continuous time fractional order systems with delays of the retarded type. Bull. Pol. Acad. Sci. Tech. 56(4), 319–324 (2008)

    Google Scholar 

  2. BusƂowicz, M.: Stability analysis of continuous-time linear systems consisting of n subsystem with different fractional orders. Bull. Pol. Acad. Sci. Tech. 60(2), 279–284 (2012)

    Google Scholar 

  3. DzieliƄski, A., Sierociuk, D., Sarwas, G.: Ultracapacitor parameters identification based on fractional order model. In: Proc. ECC 2009, Budapest (2009)

    Google Scholar 

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

    Book  MATH  Google Scholar 

  5. Ferreira, N.M.F., Machado, J.A.T.: Fractional-order hybrid control of robotic manipulators. In: Proc. 11th Int. Conf. Advanced Robotics, ICAR 2003, Coimbra, Portugal, pp. 393–398 (2003)

    Google Scholar 

  6. Kaczorek, T.: Asymptotic stability of positive fractional 2D linear systems. Bull. Pol. Acad. Sci. Tech. 57(3), 289–292 (2009)

    Google Scholar 

  7. Kaczorek, T.: Fractional positive continuous-time systems and their Reachability. Int. J. Appl. Math. Comput. Sci. 18(2), 223–228 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kaczorek, T.: Fractional positive linear systems. Kybernetes: The International Journal of Systems & Cybernetics 38(7/8), 1059–1078 (2009)

    Article  MathSciNet  Google Scholar 

  9. Kaczorek, T.: Minimum energy control of fractional positive continuous-time linear systems. In: Proc. of Conf. MMAR, Miedzyzdroje, Poland (2013)

    Google Scholar 

  10. Kaczorek, T.: Positive 1D and 2D Systems. Springer, London (2002)

    Book  MATH  Google Scholar 

  11. Kaczorek, T.: Positive linear systems consisting of n subsystems with different fractional orders. IEEE Trans. Circuits and Systems 58(6), 1203–1210 (2011)

    Article  MathSciNet  Google Scholar 

  12. Kaczorek, T.: Positive linear systems with different fractional orders. Bull. Pol. Acad. Sci. Tech. 58(3), 453–458 (2010)

    MATH  Google Scholar 

  13. Kaczorek, T.: Positivity and reachability of fractional electrical circuits. Acta Mechanica et Automatica 5(2), 42–51 (2011)

    Google Scholar 

  14. Kaczorek, T.: Selected Problems in Fractional Systems Theory. Springer, Heidelberg (2011)

    Book  Google Scholar 

  15. Kaczorek, T., Klamka, J.: Minimum energy control of 2D linear systems with variable coefficients. Int. J. of Control 44(3), 645–650 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  16. Klamka, J.: Controllability of Dynamical Systems. Kluwer Academic Press, Dordrecht (1991)

    MATH  Google Scholar 

  17. Klamka, J.: Minimum energy control of 2D systems in Hilbert spaces. System Sciences 9(1-2), 33–42 (1983)

    MathSciNet  Google Scholar 

  18. Klamka, J.: Relative controllability and minimum energy control of linear systems with distributed delays in control. IEEE Trans. Autom. Contr. 21(4), 594–595 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  19. Klamka, J.: New Trends in Nanotechology and Fractional Calculus. In: Baleanu, D., Guvenc, Z.B., Tenreiro Machado, J.A. (eds.) Controllability and minimum energy control problem of fractional discrete-time systems, pp. 503–509. Springer, New York (2010)

    Google Scholar 

  20. Klamka, J.: Controllability of dynamical systems-a survey. Archives of Control Sciences 2(3-4), 281–307 (1993)

    MathSciNet  Google Scholar 

  21. Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differenctial Equations. Willey, New York (1993)

    Google Scholar 

  22. Nishimoto, K.: Fractional Calculus. Koriama Decartess Press (1984)

    Google Scholar 

  23. Oldham, K.B., Spanier, J.: The Fractional Calculus. Academmic Press, New York (1974)

    MATH  Google Scholar 

  24. Ostalczyk, P.: The non-integer difference of the discrete-time function and its application to the control system synthesis. Int. J. Sys. Sci. 31(12), 1551–1561 (2000)

    Article  MATH  Google Scholar 

  25. Podlubny, I., Dorcak, L., Kostial, I.: On fractional derivatives, fractional order systems and PIλDÎŒ-controllers. In: Proc. 36th IEEE Conf. Decision and Control, San Diego, CA, pp. 4985–4990 (1997)

    Google Scholar 

  26. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

    MATH  Google Scholar 

  27. Sajewski, Ɓ.: Positive realization of SISO 2D different orders fractional discrete-time linear systems. Acta Mechanica et Automatica 5(2), 122–127 (2011)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Electrical Engineering, Bialystok University of Technology, Wiejska 45D, 15-351, Bialystok, Poland

    Ɓukasz Sajewski

Authors
  1. Ɓukasz Sajewski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ɓukasz Sajewski .

Editor information

Editors and Affiliations

  1. Industrial Research Institute for Automation and Measurements PIAP, Warsaw, Poland

    Roman Szewczyk

  2. Industrial Research Institute for Automation and Measurements PIAP, Warsaw, Poland

    Cezary ZieliƄski

  3. Industrial Research Institute for Automation and Measurements PIAP, Warsaw, Poland

    MaƂgorzata KaliczyƄska

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Sajewski, Ɓ. (2014). Reachability of Fractional Positive Continuous-Time Linear Systems with Two Different Fractional Orders. In: Szewczyk, R., ZieliƄski, C., KaliczyƄska, M. (eds) Recent Advances in Automation, Robotics and Measuring Techniques. Advances in Intelligent Systems and Computing, vol 267. Springer, Cham. https://doi.org/10.1007/978-3-319-05353-0_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-05353-0_24

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-05352-3

  • Online ISBN: 978-3-319-05353-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation