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Stabilization of Discrete System with Bounded Parameters

Year 2017, Volume: 18 Issue: 2, 500 - 506, 30.06.2017
https://doi.org/10.18038/aubtda.299974

Abstract

In this paper stabilization problem of linear discrete single input, single output plant by affine stabilizator is considered. It is assumed that stabilizing vector is bounded and its values are changed in a given box. We use the Schur-Szegö parameters (reflection coefficients) and obtain conditions for nonexistence and existence of a stabilizing vector.

References

  • [1] Levinson N. The Wiener RMS error criterion in filter design and prediction. J. Math. Phys., vol. 25, no. 1–4, pp. 261–278, 1946.
  • [2] Nurges Ü. New stability conditions via reflection coefficients of polynomials. IEEE Transactions on Automatic Control, vol. 50, no. 9, pp. 1354–1360, 2005.
  • [3] Büyükköroğlu T. Fixed order controller for Schur stability. Math. Comput. Appl., vol. 21, no. 2, paper no. 25, pp.1-9, 2016.
  • [4] Fam AT, Meditch JS. A canonical parameter space for linear systems design. IEEE Transactions on Automatic Control, vol. 23, no. 3, pp. 454–458, 1978.
  • [5] Petrikevich YI. Randomized methods of stabilization of the discrete linear systems. Automation and Remote Control, vol. 69, no. 11, pp. 1911–1921, 2008.
  • [6] Polyak BT, Shcherbakov PS. Hard problems in linear control theory: possible approaches to solution. Automation and Remote Control, vol. 65, no. 5, pp. 681–718, 2005.
  • [7] Nurges Ü, Avanessov S. Fixed-order stabilising controller design by a mixed randomized/deterministic method. Int. J. Control, vol. 88, no. 2, pp. 335–346, 2015.
  • [8] Büyükköroğlu T, Çelebi G, Dzhafarov V. Stabilization of discrete time systems by reflection coefficients. Tr. Inst. Math. Mekh. UrO RAN, vol. 23, no. 1, pp. 306–311, 2017.
  • [9] Waqar AM, Swaroop D, Bhattacharyya SP. Synthesis of fixed structure controllers for discrete time systems. Numerical Linear Algebra in Signals, Systems and Control. Volume 80 of the series Lecture Notes in Electrical Engineering, pp 367-385, 2011.
Year 2017, Volume: 18 Issue: 2, 500 - 506, 30.06.2017
https://doi.org/10.18038/aubtda.299974

Abstract

References

  • [1] Levinson N. The Wiener RMS error criterion in filter design and prediction. J. Math. Phys., vol. 25, no. 1–4, pp. 261–278, 1946.
  • [2] Nurges Ü. New stability conditions via reflection coefficients of polynomials. IEEE Transactions on Automatic Control, vol. 50, no. 9, pp. 1354–1360, 2005.
  • [3] Büyükköroğlu T. Fixed order controller for Schur stability. Math. Comput. Appl., vol. 21, no. 2, paper no. 25, pp.1-9, 2016.
  • [4] Fam AT, Meditch JS. A canonical parameter space for linear systems design. IEEE Transactions on Automatic Control, vol. 23, no. 3, pp. 454–458, 1978.
  • [5] Petrikevich YI. Randomized methods of stabilization of the discrete linear systems. Automation and Remote Control, vol. 69, no. 11, pp. 1911–1921, 2008.
  • [6] Polyak BT, Shcherbakov PS. Hard problems in linear control theory: possible approaches to solution. Automation and Remote Control, vol. 65, no. 5, pp. 681–718, 2005.
  • [7] Nurges Ü, Avanessov S. Fixed-order stabilising controller design by a mixed randomized/deterministic method. Int. J. Control, vol. 88, no. 2, pp. 335–346, 2015.
  • [8] Büyükköroğlu T, Çelebi G, Dzhafarov V. Stabilization of discrete time systems by reflection coefficients. Tr. Inst. Math. Mekh. UrO RAN, vol. 23, no. 1, pp. 306–311, 2017.
  • [9] Waqar AM, Swaroop D, Bhattacharyya SP. Synthesis of fixed structure controllers for discrete time systems. Numerical Linear Algebra in Signals, Systems and Control. Volume 80 of the series Lecture Notes in Electrical Engineering, pp 367-385, 2011.
There are 9 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Taner Büyükköroğlu

Vakif Dzhafarov

Publication Date June 30, 2017
Published in Issue Year 2017 Volume: 18 Issue: 2

Cite

APA Büyükköroğlu, T., & Dzhafarov, V. (2017). Stabilization of Discrete System with Bounded Parameters. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, 18(2), 500-506. https://doi.org/10.18038/aubtda.299974
AMA Büyükköroğlu T, Dzhafarov V. Stabilization of Discrete System with Bounded Parameters. AUJST-A. June 2017;18(2):500-506. doi:10.18038/aubtda.299974
Chicago Büyükköroğlu, Taner, and Vakif Dzhafarov. “Stabilization of Discrete System With Bounded Parameters”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 18, no. 2 (June 2017): 500-506. https://doi.org/10.18038/aubtda.299974.
EndNote Büyükköroğlu T, Dzhafarov V (June 1, 2017) Stabilization of Discrete System with Bounded Parameters. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 18 2 500–506.
IEEE T. Büyükköroğlu and V. Dzhafarov, “Stabilization of Discrete System with Bounded Parameters”, AUJST-A, vol. 18, no. 2, pp. 500–506, 2017, doi: 10.18038/aubtda.299974.
ISNAD Büyükköroğlu, Taner - Dzhafarov, Vakif. “Stabilization of Discrete System With Bounded Parameters”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 18/2 (June 2017), 500-506. https://doi.org/10.18038/aubtda.299974.
JAMA Büyükköroğlu T, Dzhafarov V. Stabilization of Discrete System with Bounded Parameters. AUJST-A. 2017;18:500–506.
MLA Büyükköroğlu, Taner and Vakif Dzhafarov. “Stabilization of Discrete System With Bounded Parameters”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, vol. 18, no. 2, 2017, pp. 500-6, doi:10.18038/aubtda.299974.
Vancouver Büyükköroğlu T, Dzhafarov V. Stabilization of Discrete System with Bounded Parameters. AUJST-A. 2017;18(2):500-6.