Geodesic
On the Additive $D$-Stability of Matrices on the Basis of the Kharitonov Criterion
Matematičeskie zametki, Tome 72 (2002) no. 2, pp. 265-268.

Voir la notice de l'article provenant de la source Math-Net.Ru

On the basis of the Kharitonov theorem, sufficient conditions on an $(n\times n)$ matrix $A$ are presented for the matrix $A-\operatorname {diag}(d_1,d_2,\dots ,d_n)$ to be stable for arbitrary $d_i\ge 0$, $i=\overline {1,n}$. 
@article{MZM_2002_72_2_a9,
     author = {I. M. Romanishin and L. A. Sinitskii},
     title = {On the {Additive} $D${-Stability} of {Matrices} on the {Basis} of the {Kharitonov} {Criterion}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {265--268},
     publisher = {mathdoc},
     volume = {72},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_2_a9/}
}
TY  - JOUR
AU  - I. M. Romanishin
AU  - L. A. Sinitskii
TI  - On the Additive $D$-Stability of Matrices on the Basis of the Kharitonov Criterion
JO  - Matematičeskie zametki
PY  - 2002
SP  - 265
EP  - 268
VL  - 72
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2002_72_2_a9/
LA  - ru
ID  - MZM_2002_72_2_a9
ER  - 
%0 Journal Article
%A I. M. Romanishin
%A L. A. Sinitskii
%T On the Additive $D$-Stability of Matrices on the Basis of the Kharitonov Criterion
%J Matematičeskie zametki
%D 2002
%P 265-268
%V 72
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2002_72_2_a9/
%G ru
%F MZM_2002_72_2_a9
I. M. Romanishin; L. A. Sinitskii. On the Additive $D$-Stability of Matrices on the Basis of the Kharitonov Criterion. Matematičeskie zametki, Tome 72 (2002) no. 2, pp. 265-268. http://geodesic.mathdoc.fr/item/MZM_2002_72_2_a9/

[1] Kharitonov V. L., “Ob asimptoticheskoi ustoichivosti polozheniya ravnovesiya semeistva sistem lineinykh differentsialnykh uravnenii”, Differents. uravneniya, 14:11 (1978), 2086–2088 | MR | Zbl

[2] Hershkowitz D., “Recent directions in matrix stability”, Linear Algebra Appl., 171 (1992), 161–186 | DOI | MR | Zbl

[3] Romanishin I. M., Sinitskii L. A., “$H_D$-sistemy”, Problemy upravleniya i informatiki, 1–2 (1996), 224–238 | MR

[4] Romanishin I. M., Sinitskii L. A., “O nekotorykh klassakh matrits i probleme Aizermana”, Problemy upravleniya i informatiki, 6 (1998), 14–24 | MR

[5] Kaszkurewicz E., Bhaya A., “Comments on: Necessary and Sufficient Condition for Absolute Stability of Neural Networks”, IEEE Trans. on Circuits and System, 42:8 (1995), 497–499 | DOI | MR | Zbl

[6] Pykh Yu. A., Ravnovesie i ustoichivost v modelyakh populyatsionnoi dinamiki, Nauka, M., 1983, 184 pp. | Zbl

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

[8] Gantmakher F. R., Teoriya matrits, Nauka, M., 1988, 548 pp.

[9] Sinitskii L. A., “O svoistvakh matrits, primenyaemykh v teorii elektricheskikh tsepei”, Teoreticheskaya elektrotekhnika, 1989, no. 47, 39–45 | MR

[10] Polyak B. T., Tsypkin Ya. Z., “Chastotnye kriterii robastnoi ustoichivosti i aperiodichnosti lineinykh sistem”, Avtomatika i telemekhanika, 1990, no. 9, 45–54 | MR | Zbl