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On the Local Sensitivity of the Lyapunov Equations

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Numerical Analysis and Its Applications (NAA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1988))

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Abstract

This paper presents a new local perturbation bound for the continuous-time Lyapunov matrix equations, which is not formulated in terms of condition numbers. The new bound is a nonlinear, first order homogeneous function of the absolute perturbations in the data and is sharper than the linear local bounds based on condition numbers.

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References

  1. Byers, R.: A Linpack-style condition estimator for the equation AX-XB T = C.IEEE Trans. Automat. Contr. AC-29 (1984) 926–928

    Article  MATH  MathSciNet  Google Scholar 

  2. Konstantinov, M. M., Petkov, P.Hr., Christov, N. D.: Perturbation analysis of the continuous and discrete matrix Riccati equations. Proc. 1986 ACC, Seattle, vol. 1, 636–639

    Google Scholar 

  3. M. M. Konstantinov, N. D. Christov and P. Hr.Petkov. Perturbation analysis of linear control problems. Prepr. 10th IFAC World Congress, Munich, 1987, vol. 9, 16–21

    MathSciNet  Google Scholar 

  4. Hewer, G., Kenney, C.: The sensitivity of the stable Lyapunov equation. SIAM J. Contr. Optim. 26 (1988) 321–343

    Article  MATH  MathSciNet  Google Scholar 

  5. B. Kagstrom. A perturbation analysis of the generalized Sylvester equation (AR-LB,DR-LE) = (C, F). SIAM J. Matrix Anal. Appl. 15 (1994) 1045–1060

    Article  MathSciNet  Google Scholar 

  6. Ghavimi, A., Laub, A.: Backward error, sensitivity and refinement of computed solutions of algebraic Riccati equations. Numer. Lin. Alg. Appl. 2 (1995) 29–49

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratoire d’Automatique de Grenoble, 38402 Saint Martin d’Hères, BP46, France

    Suzanne Lesecq & Alain Barraud

  2. Department of Automatics, Technical University of Sofia, 1756 Sofia, Bulgaria

    Nicolai Christov

Authors
  1. Suzanne Lesecq
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  2. Alain Barraud
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  3. Nicolai Christov
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rousse, 7000, Rousse, Bulgaria

    Lubin Vulkov  & Plamen Yalamov  & 

  2. UNI-C,Danish Computing Center for Research and Education, DTU,Building 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2001 Springer-Verlag Berlin Heidelberg

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Lesecq, S., Barraud, A., Christov, N. (2001). On the Local Sensitivity of the Lyapunov Equations. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_61

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  • DOI: https://doi.org/10.1007/3-540-45262-1_61

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41814-6

  • Online ISBN: 978-3-540-45262-1

  • eBook Packages: Springer Book Archive

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