Super-optimal Hankel-norm approximations

  • Fang-Bo Yeh
  • Lin-Fang Wei
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 183)


It is well-known that optimal Hankel-norm approximations are seldom unique for multivariable systems. This comes from the Hankel-norm being somewhat of a crude criterion for the reduction of multivariable systems. In this paper, the strengthened condition originated with N. J. Young is employed to restore the uniquess. A statespace algorithm for the computation of super-optimal solution is presented.


Hankel Operator Lyapunov Equation Hankel Matrix Multivariable System Balance Realization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    S. Y. Kung and D. W. Lin, “Optimal Hankel-norm model reductions: Multivariable systems,” IEEE Trans. Automat. Contr., vol. AC-26, pp. 832–852, 1981.CrossRefMathSciNetGoogle Scholar
  2. [2]
    K. Glover, “All optimal Hankel-norm approximations of linear multivariable system and their L error bounds,” Int. J. Contr., vol. 39, pp. 1115–1193, 1984.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    J. A. Ball and A. C. M. Ran, “Optimal Hankel-norm model reductions and Wiener-Hopf factorizations II: the noncanonical case,” Integral Eqn. Operator Theory, vol. 10, pp. 416–436, 1987.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    V. M. Adamjan, D. Z. Arov, and M. G. Krein, “Analytic properties of Schmidt pairs of a Hankel Operator and the generalized Schur-Takagi problem,” Math. of the USSR: Sborink, vol. 15, pp. 31–73, 1971.CrossRefGoogle Scholar
  5. [5]
    V. M. Adamjan, D. Z. Arov, and M. G. Krein, “Infinite block Hankel matrices and related extension problems,” AMS Transl., ser. 2, vol. 111, pp. 133–156, 1978.Google Scholar
  6. [6]
    B. A. Francis, A Course in H Control Theory. New York: Springer-Verlag, 1987.zbMATHGoogle Scholar
  7. [7]
    J. C. Doyle, “Lecture Notes in Advances in Multivariable Control,” ONR / Honeywell Workshop, Minneapolis, MN, 1984.Google Scholar
  8. [8]
    F. B. Yeh and L. F. Wei, “Inner-outer factorizations of right-invertible real-rational matrices,” Syst. Contr. Lett., vol. 14, pp. 31–36, 1990.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    N. J. Young, “The Nevanlinna-Pick problem for matrix-valued functions,” J. Operator Theory, vol. 15, pp. 239–265, 1986.zbMATHMathSciNetGoogle Scholar
  10. [10]
    N. J. Young, “Super-optimal Hankel-norm approximations,” in Modeling Robustness and Sensitivity Reduction in Control Systems, R. F. Curtain, Ed. New York: Springer-Verlag, 1987.Google Scholar
  11. [11]
    F. B. Yeh and T. S. Hwang, “A computational algorithm for the super-optimal solution of the model matching problem,” Syst. Contr. Lett., vol. 11, pp. 203–211, 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    M. C. Tsai, D. W. Gu, and I. Postlethwaite, “A state-space approach to superoptimal H control problems,” IEEE Trans. Automat. Contr., vol. AC-33, pp. 833–843, 1988.CrossRefMathSciNetGoogle Scholar
  13. [13]
    D. J. N. Limebeer, G. D. Halikias, and K. Glover, “State-space algorithm for the computation of superoptimal matrix interpolating functions,” Int. J. Contr., vol. 50, pp. 2431–2466, 1989.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Fang-Bo Yeh
    • 1
  • Lin-Fang Wei
    • 1
  1. 1.Department of MathematicsTunghai UniversityTaichungRepublic of China

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