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Existence of System Matrices with Given Spectra of Positive Stable Discrete-Time Linear Systems

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Challenges in Automation, Robotics and Measurement Techniques (ICA 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 440))

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Abstract

The problem of existence of system matrices with given spectra is addressed for positive stable discrete-time linear systems. Necessary and sufficient conditions for the existence of the system matrices are established. The considerations are illustrated by numerical examples of discrete-time linear systems.

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References

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

    Google Scholar 

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

    Book  MATH  Google Scholar 

  3. Kaczorek, T.: A class of positive and stable time-varying electrical circuits. Electr. Rev. 91(5), 121–124 (2015)

    MathSciNet  Google Scholar 

  4. Kaczorek, T.: Constructability and observability of standard and positive electrical circuits. Electr. Rev. 89(7), 132–136 (2013)

    Google Scholar 

  5. Kaczorek, T.: Positive electrical circuits and their reachability. Arch. Electr. Eng. 60(3), 283–301 (2011)

    Google Scholar 

  6. Kaczorek T.: Positive fractional linear electrical circuits. In: Proceedings of SPIE, vol. 8903. Bellingham WA, USA, Art. No 3903–35

    Google Scholar 

  7. Kaczorek, T.: Positive unstable electrical circuits. Electr. Rev. 88(5a), 187–192 (2012)

    Google Scholar 

  8. Kaczorek, T.: Zeroing of state variables in descriptor electrical circuits by state-feedbacks. Electr. Rev. 89(10), 200–203 (2013)

    Google Scholar 

  9. Kaczorek, T., Rogowski, K.: Fractional Linear Systems and Electrical Circuits. Studies in Systems, Decision and Control, vol. 13. Springer (2015)

    Google Scholar 

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

    MATH  Google Scholar 

  11. Kaczorek, T.: Positive systems consisting of n subsystems with different fractional orders. IEEE Trans. Circ. Syst.—Regul. Pap. 58(6), 1203–1210 (2011)

    Google Scholar 

  12. Kaczorek T.: Decoupling zeros of positive continuous-time linear systems and electrical circuits. Advances in Systems Science. Advances in Intelligent Systems and Computing, vol. 240, pp. 1–15. Springer (2014)

    Google Scholar 

  13. Benvenuti, L., Farina, L.: A tutorial on the positive realization problem. IEEE Trans. Auto. Control 49(5), 651–664 (2004)

    Article  MathSciNet  Google Scholar 

  14. Kaczorek T.: Linear Control Systems, vol. 1. Research Studies Press, Wiley, New York (1992)

    Google Scholar 

  15. Kaczorek, T., Sajewski, Ł.: Realization Problem for Positive and Fractional Systems. Springer (2014)

    Google Scholar 

  16. Shaked, U., Dixon, M.: Generalized minimal realization of transfer-function matrices. Int. J. Control 25(5), 785–803 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  17. Kaczorek, T.: A modified state variables diagram method for determination of positive realizations of linear continuous-time systems with delays. Int. J. Appl. Math. Comput. Sci. 22(4), 897–905 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  18. Kaczorek, T.: A realization problem for positive continuous-time linear systems with reduced numbers of delays. Int. J. Appl. Math. Comput. Sci. 16(3), 325–331 (2006)

    MathSciNet  MATH  Google Scholar 

  19. Kaczorek, T.: Computation of positive stable realizations for discrete-time linear systems. Comput. Prob. Electr. Eng. 2(1), 41–48 (2012)

    MathSciNet  Google Scholar 

  20. Kaczorek, T.: Computation of positive stable realizations for linear continuous-time systems. Bull. Pol. Acad. Techn. Sci. 59(3), 273–281 (2011)

    MATH  Google Scholar 

  21. Kaczorek, T.: Computation of realizations of discrete-time cone systems. Bull. Pol. Acad. Sci. Techn. 54(3), 347–350 (2006)

    MATH  Google Scholar 

  22. Kaczorek, T.: Positive minimal realizations for singular discrete-time systems with delays in state and delays in control. Bull. Pol. Acad. Sci. Technol. 53(3), 293–298 (2005)

    MATH  Google Scholar 

  23. Kaczorek, T.: Positive stable realizations of discrete-time linear systems. Bull. Pol. Acad. Sci. Techn. 60(3), 605–616 (2012)

    Google Scholar 

  24. Kaczorek, T.: Positive stable realizations with system Metzler matrices. Arch. Control Sci. 21(2), 167–188 (2011)

    MathSciNet  MATH  Google Scholar 

  25. Kaczorek, T.: Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs. Int. J. Appl. Math. Comput. Sci. 16(2), 101–106 (2006)

    MathSciNet  Google Scholar 

  26. Kaczorek, T.: Positive and asymptotically stable realizations for descriptor discrete-time linear systems. Bull. Pol. Acad. Sci. Technol. 61(1), 229–237 (2013)

    MathSciNet  Google Scholar 

  27. Kaczorek, T.: Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems. Arch. Control Sci. 22(4), 371–384 (2012)

    Google Scholar 

  28. Kaczorek, T.: Positive realizations with reduced numbers of delays for 2-D continuous-discrete linear systems. Bull. Pol. Acad. Sci. Technol. 60(4), 835–840 (2012)

    Google Scholar 

  29. Kaczorek, T.: Positive stable realizations for fractional descriptor continuous-time linear systems. Arch. Control Sci. 22(3), 255–265 (2012)

    MathSciNet  Google Scholar 

  30. Kaczorek, T.: Positive stable realizations of fractional continuous-time linear systems. Int. J. Appl. Math. Comput. Sci. 21(4), 697–702 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  31. Kaczorek, T.: Realization problem for fractional continuous-time systems. Arch. Control Sci. 18(1), 43–58 (2008)

    MathSciNet  MATH  Google Scholar 

  32. Kaczorek, T.: Determination of the set of Metzler matrices for given stable polynomials. Measur. Aut. Monit. 58(5), 407–412 (2012)

    Google Scholar 

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Acknowledgment

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

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Correspondence to Tadeusz Kaczorek .

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Kaczorek, T., Borawski, K. (2016). Existence of System Matrices with Given Spectra of Positive Stable Discrete-Time Linear Systems. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds) Challenges in Automation, Robotics and Measurement Techniques. ICA 2016. Advances in Intelligent Systems and Computing, vol 440. Springer, Cham. https://doi.org/10.1007/978-3-319-29357-8_14

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  • DOI: https://doi.org/10.1007/978-3-319-29357-8_14

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  • Online ISBN: 978-3-319-29357-8

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