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A Generalized KYP Lemma-Based Approach for H ∞ Control of Singularly Perturbed Systems

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Abstract

In this paper, H ∞ control synthesis of linear time invariant singularly perturbed systems (SPS) based on a generalized KYP lemma approach is investigated. By employing a generalized KYP lemma on the low- and high-frequency domains of SPS, respectively, a slow (low-frequency) controller and a fast (high-frequency) controller are designed to stabilize the slow and fast subsystems, and also to meet the individual H ∞ performance specifications. A composite controller for the full-order SPS is constructed via the above two above well-defined lower-order problems. Moreover, the effectiveness of the proposed method is verified as compared with the traditional H ∞ design method by its application to a tracking problem of SPS and an H ∞ model matching problem for SPS.

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References

  1. C.T. Chen, Linear System Theory and Design (Holt Rinehart & Winston, New York, 1984)

    Google Scholar 

  2. V. Dragan, Asymptotic expansions for game-theoretic Riccati equations and stabilization with disturbance attenuation for singularly perturbed systems. Syst. Control Lett. 20(6), 455–463 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  3. V. Dragan, P. Shi, E.K. Boukas, Control of singularly perturbed system with Markovian jump parameters: An H ∞ approach. Automatica 35, 1359–1378 (1999)

    Article  MathSciNet  Google Scholar 

  4. E. Fridman, Near-optimal H ∞ control of linear singularly perturbed systems. IEEE Trans. Automat. Control 41(2), 236–240 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  5. E. Fridman, State-feedback H ∞ control of nonlinear singularly perturbed systems. Int. J. Robust Nonlinear Control 6, 25–45 (2001)

    MathSciNet  Google Scholar 

  6. C. Gong, B. Su, Robust H ∞ filtering of convex polyhedral uncertain time-delay fuzzy systems. Int. J. Innov. Comput. Inf. Control 4(4), 793–802 (2008)

    Google Scholar 

  7. T. Iwasaki, S. Hara, Robust control synthesis with general frequency domain specifications: static gain feedback case. In: Proc. Amer. Control Conf. (2004)

  8. T. Iwasaki, S. Hara, Generalized KYP lemma: unified frequency domain inequalities with design applications. IEEE Trans. Automat. Control 50, 41–59 (2005)

    Article  MathSciNet  Google Scholar 

  9. T. Iwasaki, S. Hara, Feedback control synthesis of multiple frequency domain specifications via generalized KYP lemma. Int. J. Robust Nonlinear Control 17, 415–434 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  10. T. Iwasaki, S. Hara, A.L. Fradkov, Time domain interpretations of frequency domain inequalities on (semi) finite ranges. Syst. Control Lett. 54, 681–691 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  11. H.K. Khail, Output feedback control of linear two-time-scale systems. IEEE Trans. Automat. Control 32, 784–792 (1987)

    Article  MathSciNet  Google Scholar 

  12. H.K. Khail, F.C. Chen, H ∞ control of two-time-scale systems. Syst. Control Lett. 19, 35–42 (1992)

    Article  Google Scholar 

  13. P.V. Kokotovic, H.K. Khalil, J. O’Reilly, Singular Perturbation Methods in Control: Analysis and Design (Academic Press, New York, 1986)

    MATH  Google Scholar 

  14. D.W. Luse, Frequency domain results for systems with multiple time scales. IEEE Trans. Automat. Control 31, 918–924 (1986)

    Article  MATH  Google Scholar 

  15. D.W. Luse, J.A. Ball, Frequency-scale decomposition of H ∞ disk problems. SIAM J. Control Optim. 27, 814–835 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  16. D.W. Luse, H.K. Khail, Frequency domain results for systems with slow and fast dynamics. IEEE Trans. Automat. Control 30, 1171–1179 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  17. H.M. Oloomi, M.E. Sawan, H ∞ model matching problem for singularly perturbed systems. Automatica 32, 369–377 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  18. Z. Pan, T. Basar, H ∞ optimal control for singularly perturbed systems Pan I: Perfect state measurements. Automatica 29, 401–423 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  19. Z. Pan, T. Basar, H ∞ optimal control for singularly perturbed systems Part II: Imperfect state measurements. IEEE Trans. Automat. Control 39, 280–299 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  20. A. Rantzer, On the Kalman–Yakubovich–Popov lemma. Syst. Control Lett. 28(1), 7–10 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  21. T.L. Shen, H ∞ Control Theory and Applications (Tsinghua University Press, Beijing, 1996)

    Google Scholar 

  22. P. Shi, V. Dragan, Asymptotic H ∞ control of singularly perturbed system with parametric uncertainties. IEEE Trans. Automat. Control 44, 1738–1742 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  23. W. Tan, T. Leung, Q. Tu, H ∞ control for singularly perturbed systems. Automatica 34, 255–260 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  24. Y. Wang, Z. Sun, H ∞ control of networked control system via LMI approach. Int. J. Innov. Comput. Inf. Control 3(2), 343–352 (2007)

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Information & Control, Nanjing University of Information Science and Technology, Nanjing, 210044, Jiangsu, P.R. China

    Ping Mei

  2. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu, P.R. China

    Ping Mei, Chenxiao Cai & Yun Zou

Authors
  1. Ping Mei
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  2. Chenxiao Cai
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  3. Yun Zou
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Corresponding author

Correspondence to Yun Zou.

Additional information

This work was supported by National Natural Science Foundation of China (No. 60874007) and Research Fund for the Doctoral Program of Higher Education of China (No. 200802550024).

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Mei, P., Cai, C. & Zou, Y. A Generalized KYP Lemma-Based Approach for H ∞ Control of Singularly Perturbed Systems. Circuits Syst Signal Process 28, 945–957 (2009). https://doi.org/10.1007/s00034-009-9125-4

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  • DOI: https://doi.org/10.1007/s00034-009-9125-4

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