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Recent Advances in Automation, Robotics and Measuring Techniques pp 307–316Cite as

Pointwise Completeness and Pointwise Degeneracy of Linear Continuous-Time Systems with Different Fractional Orders

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

Abstract

In the paper the positive linear continuous-time systems with different fractional orders described by homogeneous state equations are considered. Definition and necessary and sufficient conditions for the pointwise completeness and the pointwise degeneracy are given. The considerations are illustrated by examples.

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References

  1. Busłowicz, M.: Punktowa zupełność i punktowa degeneracja liniowych układów dyskretnych ułamkowego rzędu. Zesz. Nauk. Politechniki Śląskiej, ser. Automatyka 151, 17–29 (2008)

    Google Scholar 

  2. Busłowicz, M., Kociszewski, R., Trzasko, W.: Punktowa degeneracja i punktowa zupełność liniowych dodatnich układów dyskretnych z opóźnieniami. Zesz. Nauk. Politechniki Śląskiej, ser. Automatyka 145, 51–56 (2006)

    Google Scholar 

  3. Choundhury, A.K.: Necessary and sufficient conditions of pointwise completeness of linear time-invariant delay-differential systems. Int. J. Control 16(6), 1083–1100 (1972)

    Article  Google Scholar 

  4. Kaczorek, T.: Positive linear systems consisting of n subsystems with different fractional orders. IEEE Trans. Circ. Sys. I 58(6), 1203–1210 (2011)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  6. Kaczorek, T.: Pointwise completeness and pointwise degeneracy of standard and positive hybrid systems described by the general model. Archives of Control Sciences 20(2), 121–131 (2010)

    Google Scholar 

  7. Kaczorek, T., Busłowicz, M.: Pointwise completeness and pointwise degeneracy of linear continuous-time fractional order systems. JAMRIS 3(1), 8–11 (2009)

    Google Scholar 

  8. Kaczorek, T.: Wybrane zagadnienia teorii układów niecałkowitego rzędu, Oficyna Wydawnicza Politechniki Białostockiej, Białystok (2009)

    Google Scholar 

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

    Book  MATH  Google Scholar 

  10. Miller, K.S., Ross, B.: An Introduction to the fractional calculus and fractional differential equations. Willey, New York (1993)

    MATH  Google Scholar 

  11. Podlubny, I.: Matrix approach to discrete fractional calculus. An International Journal for Theory and Applications 3(4), 359–386 (2000)

    MATH  MathSciNet  Google Scholar 

  12. Popov, V.M.: Pointwise degeneracy of linear time-invariant delay-differential equations. J. Diff. Equation 11, 541–561 (1972)

    Article  MATH  Google Scholar 

  13. Trzasko, W.: Punktowa zupełność i punktowa degeneracja układów dyskretnych niecałkowitego rzędu. In: Automation 2012, Pomiary Automatyka Robotyka, vol. 2, pp. 332–337 (2012)

    Google Scholar 

  14. Trzasko, W.: Względna punktowa zupełność dodatnich układów ciągło-dyskretnych niecałkowitego rzędu. In: Automation 2011, Pomiary Automatyka Robotyka, vol. 2, pp. 528–537 (2011)

    Google Scholar 

  15. Trzasko, W., Busłowicz, M., Kaczorek, T.: Pointwise completeness of discrete-time cone systems with delays. In: Proc. of EUROCON 2007, pp. 606–611. IEEE Xplore (2007)

    Google Scholar 

  16. Weiss, L.: Controllability for various linear and nonlinear systems models. In: Seminar on Differential Equations and Dynamic System. Lecture Notes in Mathematics, vol. 144, pp. 250–262. Springer, Heidelberg (1970)

    Chapter  Google Scholar 

  17. Vinagre, B.M.: Fractional Calculus Fundamentals. Tutorial Workshop #2. Fractional Calculus Applications in Automatic Control and Robotics. In: 41st IEEE Conference on Decision and Control, Las Vegas (2002)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Electrical Engineering, Bialystok University of Technology, Białystok, Poland

    Wojciech Trzasko

Authors
  1. Wojciech Trzasko
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Correspondence to Wojciech Trzasko .

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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

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Trzasko, W. (2014). Pointwise Completeness and Pointwise Degeneracy of Linear Continuous-Time Systems with Different Fractional Orders. In: Szewczyk, R., Zieliński, C., Kaliczyńska, 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_30

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  • DOI: https://doi.org/10.1007/978-3-319-05353-0_30

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-05352-3

  • Online ISBN: 978-3-319-05353-0

  • eBook Packages: EngineeringEngineering (R0)

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