The D -stability problem for 4 × 4 real matrices

Serkan T. Impram; Russell Johnson; Raffaella Pavani

Archivum Mathematicum (2005)

  • Volume: 041, Issue: 4, page 439-450
  • ISSN: 0044-8753

Abstract

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We give detailed discussion of a procedure for determining the robust D -stability of a 4 × 4 real matrix. The procedure begins from the Hurwitz stability criterion. The procedure is applied to two numerical examples.

How to cite

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Impram, Serkan T., Johnson, Russell, and Pavani, Raffaella. "The $D$-stability problem for $4\times 4$ real matrices." Archivum Mathematicum 041.4 (2005): 439-450. <http://eudml.org/doc/249510>.

@article{Impram2005,
abstract = {We give detailed discussion of a procedure for determining the robust $D$-stability of a $4\times 4$ real matrix. The procedure begins from the Hurwitz stability criterion. The procedure is applied to two numerical examples.},
author = {Impram, Serkan T., Johnson, Russell, Pavani, Raffaella},
journal = {Archivum Mathematicum},
keywords = {diagonal stability; Cauchy indices; diagonal stability; Cauchy indices},
language = {eng},
number = {4},
pages = {439-450},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {The $D$-stability problem for $4\times 4$ real matrices},
url = {http://eudml.org/doc/249510},
volume = {041},
year = {2005},
}

TY - JOUR
AU - Impram, Serkan T.
AU - Johnson, Russell
AU - Pavani, Raffaella
TI - The $D$-stability problem for $4\times 4$ real matrices
JO - Archivum Mathematicum
PY - 2005
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 041
IS - 4
SP - 439
EP - 450
AB - We give detailed discussion of a procedure for determining the robust $D$-stability of a $4\times 4$ real matrix. The procedure begins from the Hurwitz stability criterion. The procedure is applied to two numerical examples.
LA - eng
KW - diagonal stability; Cauchy indices; diagonal stability; Cauchy indices
UR - http://eudml.org/doc/249510
ER -

References

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  1. Abed E. H., Decomposition and stability of multiparameter singular perturbation problems, IEEE Trans. Automat. Control, AC-31 (1986), 925–934. (1986) Zbl0601.93004
  2. Barker G. P., Berman A., Plemmons R. J., Positive diagonal solutions to the Lyapunov equations, Linear and Multilinear Algebra 5 (1978), 249–256. (1978) Zbl0385.15006MR0469939
  3. Berman A., Shasha D., Inertia-preserving matrices, SIAM J. Matrix Anal. Appl. 12-2 (1991), 209–212. (1991) Zbl0733.15004MR1089156
  4. Cain B., Real 3 × 3 D -stable matrices, J. Res. of the National Bureau of Standards, Sec. B 80 (1976), 75–77. (1976) MR0419478
  5. Cain B., Inside the D -stable matrices, Linear Algebra Appl. 56 (1984), 237–243. (1984) Zbl0525.15008MR0724564
  6. Cross G. W., Three types of matrix stability, Linear Algebra Appl. 20 (1978), 253–263. (1978) Zbl0376.15007MR0480586
  7. Chen J., Fan M. K. H., Yu C., On D -stability and structured singular values, Systems Control Lett. 24 (1995), 19–24. (1995) Zbl0877.93079MR1307123
  8. Carlson D., Datta B. N., Johnson C. R., A semi-definite Lyapunov theorem and the characterization of tridiagonal D -stable matrices, SIAM J. Algebraic Discrete Methods 3 (1982), 293–304. (1982) Zbl0541.15008MR0666854
  9. Gantmacher F. R., The theory of matrices II, Chelsea Publishing Company, 1959. (1959) MR0107649
  10. Hartfiel D. J., Concerning the interior of D -stable matrices, Linear Algebra Appl. 30 (1980), 201–207. (1980) MR0568792
  11. Hershkowitz D., Recent direction in matrix stability, Linear Algebra Appl. 171 (1992), 161–186. (1992) MR1165452
  12. Horn R. A., Johnson C. R., Topics in matrix analysis, Cambridge University Press, 1991. (1991) Zbl0729.15001MR1091716
  13. Johnson C. R., Second, third, and fourth order D -stability, J. Res. of the National Bureau of Standards, Sec. B 78 (1974), 11–13. (1974) Zbl0283.15005MR0340287
  14. Johnson R., Tesi A., On the D -stability problem for real matrices, Boll. Unione Mat. Ital., Sez. B, Artic. Ric. Mat. (8) 2, No. 2 (1999), 299–314. (1999) Zbl0936.15014MR1706600
  15. Kanovei G. V., Logofet D. O., D -stability of 4 × 4 matrices, J. Comput. Math. Math. Phys. 38 (1998), 1369–1374. (1998) MR1669150
  16. Seidenberg A., A new decision procedure for elementary algebra, Ann. Math. (2) 60 (1954), 365–374. (1954) MR0063994

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