International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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New Upper Bounds for the CALE: A Singular Value Decomposition Approach

  • Savov, Svetoslav G. (Institute of Information Technologies, Bulgarian Academy of Sciences, Acad.) ;
  • Popchev, Ivan P. (Institute of Information Technologies, Bulgarian Academy of Sciences, Acad.)
  • Published : 2008.04.30
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Abstract

Motivated by the fact that upper solution bounds for the continuous Lyapunov equation are valid under some very restrictive conditions, an attempt is made to extend the set of Hurwitz matrices for which such bounds are applicable. It is shown that the matrix set for which solution bounds are available is only a subset of another stable matrices set. This helps to loosen the validity restriction. The new bounds are illustrated by examples.

Keywords

References

  1. Y. Fang, K. Loparo, and X. Feng, "New estimates for solutions of Lyapunov equations," IEEE Trans. on Automatic Control, vol. 42, no. 3, pp. 408-411, March 1997 https://doi.org/10.1109/9.557586
  2. R. Horn and C. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991
  3. N. Komaroff, "Upper summation and product bounds for solution eigenvalues of the Lyapunov matrix equation," IEEE Trans. on Automatic Control, vol. 37, no. 5, pp. 337-341, May 1992
  4. W. Kwon, Y. Moon, and S. Ahn, "Bounds in algebraic Riccati and Lyapunov equations: A survey and some new results," International Journal of Control, vol. 64, no. 3, pp. 377-389, March 1996 https://doi.org/10.1080/00207179608921634
  5. T. Mori and I. Derese, "A brief summary of the bounds on the solution of the algebraic matrix equations in control theory," International Journal of Control, vol. 39, no. 2, pp. 247-256, February 1984 https://doi.org/10.1080/00207178408933163
  6. T. Mori and H. Kokame, "On solution bounds for three types of Luapunov matrix equations: Continuous, discrete and unified equations," IEEE Trans. on Automatic Control, vol. 47, no. 10, pp. 1767-1770, October 2002 https://doi.org/10.1109/TAC.2002.803557
  7. S. Savov and I. Popchev, "New upper estimates for the solution of the CALE," IEEE Trans. on Automatic Control, vol. 49, no. 10, pp. 1841-1842, October 2004 https://doi.org/10.1109/TAC.2004.835587
  8. M. Tippett and D. Marchesin, "Upper bounds for the solution of the discrete algebraic Lyapunov equation," Automatica, vol. 35, no. 8, pp. 1485-1489, 1999 https://doi.org/10.1016/S0005-1098(99)00041-2
  9. K. Yasuda and K. Hirai, "Upper and lower bounds on the solution of the algebraic matrix Riccati and Lyapunov equation," IEEE Trans. on Automatic Control, vol. 24, no. 6, pp. 483-487, June 1979 https://doi.org/10.1109/TAC.1979.1102075