Skip to main content
SpringerLink
Log in
Book cover

International Conference Automation

ICA 2017: Automation 2017 pp 45–57Cite as

Descriptor Fractional Continuous-Time Linear System and Its Solution – Comparison of Three Different Methods

  • Conference paper
  • First Online:

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 550))

Abstract

Descriptor fractional continuous-time linear systems are addressed. Three different methods for finding the solution to the state equation of the descriptor fractional linear system are considered. The methods are based on: Shuffle algorithm, Drazin inverse of the matrices and Weierstrass-Kronecker decomposition theorem. Effectiveness of the methods is demonstrated on simple numerical example.

This is a preview of subscription content, 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 EPUB and 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

Learn about institutional subscriptions

References

  1. Campbell, S.L., Meyer, C.D., Rose, N.J.: Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients. SIAMJ. Appl. Math. 31(3), 411–425 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  2. Dai, L.: Singular Control Systems. LNCIS. Springer, Berlin (1989). doi:10.1007/BFb0002475

    Book  MATH  Google Scholar 

  3. Dodig, M., Stosic, M.: Singular systems state feedbacks problems. Linear Algebra Appl. 431(8), 1267–1292 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dzieliński, A., Sierociuk, D., Sarwas, G.: Ultracapacitor parameters identification based on fractional order model. In: Proceedings of the ECC, Budapest (2009)

    Google Scholar 

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

    Google Scholar 

  6. Guang-Ren, D.: Analysis and Design of Descriptor Linear Systems. Springer, New York (2010)

    MATH  Google Scholar 

  7. Kaczorek, T.: Application of Drazin inverse to analysis of descriptor fractional discrete-time linear systems with regular pencils. Int. J. Appl. Math. Comput. Sci. 23(1), 29–33 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kaczorek, T.: Descriptor fractional linear systems with regular pencils. Int. J. Appl. Math. Comput. Sci. 23(2), 309–315 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kaczorek, T.: Drazin inverse matrix method for fractional descriptor continuous-time linear systems. Bull. Pol. Acad. Sci. Tech. Sci. 62(3), 409–412 (2014)

    Google Scholar 

  10. Kaczorek, T.: Reduction and decomposition of singular fractional discrete-time linear systems. Acta Mechanica Automatica 5(4), 1–5 (2011)

    Google Scholar 

  11. Kaczorek, T.: Selected Problems in Fractional Systems Theory. Springer, Berlin (2011)

    Book  MATH  Google Scholar 

  12. Kaczorek, T.: Singular fractional continuous-time and discrete-time linear systems. Acta Mechanica Automatica 7(1), 26–33 (2013)

    Article  Google Scholar 

  13. Kaczorek, T.: Singular fractional discrete-time linear systems. Control Cybern. 40(3), 1–8 (2011)

    MathSciNet  MATH  Google Scholar 

  14. Kaczorek, T.: Solution of the state equations of descriptor fractional discrete-time linear systems with regular pencils. Tech. Transp. Szyn. (10), 415–422 (2013)

    Google Scholar 

  15. Kaczorek, T.: Vectors and Matrices in Automation and Electrotechnics. WNT, Warszawa (1998)

    Google Scholar 

  16. Losada, J., Nieto, J.: Properties of a new fractional derivative without singular kernel. Progr. Fract. Differ. Appl. 1(2), 87–92 (2015)

    Google Scholar 

  17. Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  21. Sajewski, Ł.: Descriptor fractional discrete-time linear system and its solution—comparison of three different methods. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds.) Challenges in Automation, Robotics and Measurement Techniques. AISC, vol. 440, pp. 37–50. Springer, Heidelberg (2016). doi:10.1007/978-3-319-29357-8_4

    Chapter  Google Scholar 

  22. Sajewski, Ł.: Solution of the state equation of descriptor fractional continuous-time linear systems with two different fractional. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds.) Progress in Automation, Robotics and Measuring Techniques. AISC, vol. 350, pp. 233–242. Springer, Heidelberg (2016). doi:10.1007/978-3-319-15796-2_24

    Google Scholar 

Download references

Acknowledgments

This work was supported by National Science Centre in Poland under work No. 2014/13/B/ST7/03467.

Author information

Authors and Affiliations

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

    Łukasz Sajewski

Authors
  1. Łukasz Sajewski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Łukasz 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 Zieliński

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

    Małgorzata Kaliczyńska

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Sajewski, Ł. (2017). Descriptor Fractional Continuous-Time Linear System and Its Solution – Comparison of Three Different Methods. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds) Automation 2017. ICA 2017. Advances in Intelligent Systems and Computing, vol 550. Springer, Cham. https://doi.org/10.1007/978-3-319-54042-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-54042-9_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54041-2

  • Online ISBN: 978-3-319-54042-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation