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Stabilizability analysis of sphere plants

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Abstract

Let p(s, δ) be a sphere plant family described by the transfer function set where the coefficients of the denominator and numerator polynomials are affine in a real uncertain parameter vector δ satisfying the euclidean norm constraint ‖δ‖<δ. The concept of stabilizability radius of P(s, δ) is introduced which is the norm bound δ s for δ such that every member plant of P(s, δ) is stabilizable if and only if ‖δ‖<δ s. The stabilizability radius can be simply interpreted as the ‘largest sphere’ around the nominal plant P(s, 0) such that P(s, δ) is stabilizable. The numerical method and the analytical method are presented to solve the stabilizability radius calculation problem of the sphere plants.

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References

  1. CHAPELLAT H, BHATTACHARYYA S P. A generalization of Kharitonov’s theorem: Robust stability of interval plants [J]. IEEE Transaction on Automatic Control, 1989, 34(3): 306–311.

    Article  MathSciNet  MATH  Google Scholar 

  2. BARMISH B R, HOLLOT C V, KRAUS F J, TEMPO R. Extreme point results for robust stabilization of interval plants with first order compensators [J]. IEEE Transaction on Automatic Control, 1992, 37(6): 707–714.

    Article  MathSciNet  MATH  Google Scholar 

  3. BARMISH B R. New tools for robustness of linear systems [M]. New York: MacMillan Publishing Company, 1994: 113–125.

    Google Scholar 

  4. QIU L, DAVISON E J. A simple procedure for the exact stability robustness computation of polynomials with affine coefficient perturbations [J]. Systems & Control Letters, 1989, 13(5): 413–420.

    Article  MathSciNet  MATH  Google Scholar 

  5. WU Qing-he. Computation of the stability radius of a Hurwitz polynomial with diamond-like uncertainties [J]. System & Control Letters, 1998, 35(1): 45–60.

    Article  MATH  Google Scholar 

  6. WU Qing-he, MANSOUR M. Robust stability analysis of control systems with parameter uncertainties: An eigenvalue approach [C]// Proceedings of the 14th World Congress of IFAC. Beijing, China, 1999: 49–54.

  7. WU Qing-he. Robust stability analysis of control systems with interval plants [J]. International Journal of Control, 2001, 74(9): 921–937.

    Article  MathSciNet  MATH  Google Scholar 

  8. LÜ Bin, WU Qing-he. Stability margin of the uncertain control system [J]. Journal of Control Theory and Applications, 2009, 7(4): 427–432.

    Article  Google Scholar 

  9. VIDYASAGAR M. Control system synthesis: A factorization approach [M]. Cambridge, Massachusetts: MIT Press, 1985: 78–82.

  10. BLONDEL V. Simultaneous stabilization of linear systems [M]. New York: Macmillan, 1994: 131–145.

    Book  Google Scholar 

  11. BLONDEL V, GEVERS M. Simultaneous stabilizability of three linear systems is rationally undecidable [J]. Mathematics of Control, Signals and Systems, 1993, 6(2): 135–145.

    Article  MathSciNet  MATH  Google Scholar 

  12. BLONDEL V, TSITSIKLIS J. NP-hardness of some linear control design problems [J]. SIAM Journal on Control and Optimization, 1997, 35(6): 2118–2127.

    Article  MathSciNet  MATH  Google Scholar 

  13. WU Qing-he, XU Li, YOSHIHISA A. On the necessary solvability conditions of parametric robust stabilization problem [J]. Acta Automatica Sinica, 2004, 30(5): 723–730.

    MathSciNet  Google Scholar 

  14. BARMISH B R. On the radius of stabilizability of LTI systems: Application to projection implementation in indirect adaptive control [J]. International Journal of Adaptive Control and Signal Processing, 1991, 5(4): 251–258.

    Article  MATH  Google Scholar 

  15. WU Qing-he. Stabilizability may be sufficient for robustly stabilizing an interval plant [J]. Acta Automatica Sinica, 2007, 33(10): 1084–1087.

    MathSciNet  Google Scholar 

  16. WU Qing-he. Solvability condition for a class of parametric robust stabilization problem [J]. Journal of Beijing Institute of Technology, 2007, 16(4): 379–383.

    MathSciNet  MATH  Google Scholar 

  17. LÜ Bin, WU Qing-he, XU Li. Optimal robust stabilization for sphere plant family [J]. Control Theory & Applications, 2010, 27(11): 1497–1503. (in Chinese)

    MATH  Google Scholar 

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Authors and Affiliations

  1. School of Guanghua Management, Peking University, Beijing, 100871, China

    Bin Lü  (吕斌)

  2. Baoshang Bank Post-Doctoral Research Center, Baoshang Bank, Beijing, 100101, China

    Bin Lü  (吕斌)

  3. School of Automation, Beijing Institute of Technology, Beijing, 100081, China

    Qing-he Wu  (伍清河)

  4. Department of Electronics and Information Systems, Akita Prefectural University, Yuri-Honjo, Akita, 015-0055, Japan

    Li Xu  (徐粒)

  5. No. 208 Research Institute of China Ordnance Industries, Beijing, 102202, China

    Yang Yang  (杨洋)

Authors
  1. Bin Lü  (吕斌)
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  2. Qing-he Wu  (伍清河)
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  3. Li Xu  (徐粒)
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  4. Yang Yang  (杨洋)
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Corresponding author

Correspondence to Bin Lü  (吕斌).

Additional information

Foundation item: Project(JSPS.KAKENHI22560451) supported by the Japan Society for the Promotion of Science; Project(69904003) supported by the National Natural Science Foundation of China; Project(YJ0267016) supported by the Advanced Ordnance Research Supporting Fund of China

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Lü, B., Wu, Qh., Xu, L. et al. Stabilizability analysis of sphere plants. J. Cent. South Univ. 19, 2561–2571 (2012). https://doi.org/10.1007/s11771-012-1311-z

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  • DOI: https://doi.org/10.1007/s11771-012-1311-z

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