Geodesic
The $D$-stability problem for $4\times 4$ real matrices
Archivum mathematicum, Tome 41 (2005) no. 4, pp. 439-450
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 15A04, 15A18, 34D15, 65F15, 93D09
Keywords: diagonal stability; Cauchy indices 
@article{ARM_2005_41_4_a7,
     author = {Impram, Serkan T. and Johnson, Russell and Pavani, Raffaella},
     title = {The $D$-stability problem for $4\times 4$ real matrices},
     journal = {Archivum mathematicum},
     pages = {439--450},
     year = {2005},
     volume = {41},
     number = {4},
     mrnumber = {2195496},
     zbl = {1122.15003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2005_41_4_a7/}
}
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
SP  - 439
EP  - 450
VL  - 41
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ARM_2005_41_4_a7/
LA  - en
ID  - ARM_2005_41_4_a7
ER  - 
%0 Journal Article
%A Impram, Serkan T.
%A Johnson, Russell
%A Pavani, Raffaella
%T The $D$-stability problem for $4\times 4$ real matrices
%J Archivum mathematicum
%D 2005
%P 439-450
%V 41
%N 4
%U http://geodesic.mathdoc.fr/item/ARM_2005_41_4_a7/
%G en
%F ARM_2005_41_4_a7
Impram, Serkan T.; Johnson, Russell; Pavani, Raffaella. The $D$-stability problem for $4\times 4$ real matrices. Archivum mathematicum, Tome 41 (2005) no. 4, pp. 439-450. http://geodesic.mathdoc.fr/item/ARM_2005_41_4_a7/

[1] Abed E. H.: Decomposition and stability of multiparameter singular perturbation problems. IEEE Trans. Automat. Control, AC-31 (1986), 925–934. | Zbl

[2] Barker G. P., Berman A., Plemmons R. J.: Positive diagonal solutions to the Lyapunov equations. Linear and Multilinear Algebra 5 (1978), 249–256. | MR | Zbl

[3] Berman A., Shasha D.: Inertia-preserving matrices. SIAM J. Matrix Anal. Appl. 12-2 (1991), 209–212. | MR | Zbl

[4] Cain B.: Real $3\times 3$ $D$-stable matrices. J. Res. of the National Bureau of Standards, Sec. B 80 (1976), 75–77. | MR

[5] Cain B.: Inside the $D$-stable matrices. Linear Algebra Appl. 56 (1984), 237–243. | MR | Zbl

[6] Cross G. W.: Three types of matrix stability. Linear Algebra Appl. 20 (1978), 253–263. | MR | Zbl

[7] Chen J., Fan M. K. H., Yu C.: On $D$-stability and structured singular values. Systems Control Lett. 24 (1995), 19–24. | MR | Zbl

[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. | MR | Zbl

[9] Gantmacher F. R.: The theory of matrices II. Chelsea Publishing Company, 1959. | MR

[10] Hartfiel D. J.: Concerning the interior of $D$-stable matrices. Linear Algebra Appl. 30 (1980), 201–207. | MR

[11] Hershkowitz D.: Recent direction in matrix stability. Linear Algebra Appl. 171 (1992), 161–186. | MR

[12] Horn R. A., Johnson C. R.: Topics in matrix analysis. Cambridge University Press, 1991. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[15] Kanovei G. V., Logofet D. O.: $D$-stability of $4\times 4$ matrices. J. Comput. Math. Math. Phys. 38 (1998), 1369–1374. | MR

[16] Seidenberg A.: A new decision procedure for elementary algebra. Ann. Math. (2) 60 (1954), 365–374. | MR