Geodesic
Eeffective criteria of exponential stability of autonomous difference equations
Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 402-414 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We obtain stability criteria for several classes of linear autonomous difference equations. The criteria are expressed in explisit analytic form, as well as in the form of belonging values of a vector function of the equation parameters to a domain in three-dimensional space.
Keywords: difference equation, stability, stability domain, Schur-Cohn polynomial. 
@article{VTAMU_2018_23_123_a7,
     author = {A. A. Kandakov and K. M. Chudinov},
     title = {Eeffective criteria of exponential stability of autonomous difference equations},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {402--414},
     year = {2018},
     volume = {23},
     number = {123},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a7/}
}
TY  - JOUR
AU  - A. A. Kandakov
AU  - K. M. Chudinov
TI  - Eeffective criteria of exponential stability of autonomous difference equations
JO  - Vestnik rossijskih universitetov. Matematika
PY  - 2018
SP  - 402
EP  - 414
VL  - 23
IS  - 123
UR  - http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a7/
LA  - ru
ID  - VTAMU_2018_23_123_a7
ER  - 
%0 Journal Article
%A A. A. Kandakov
%A K. M. Chudinov
%T Eeffective criteria of exponential stability of autonomous difference equations
%J Vestnik rossijskih universitetov. Matematika
%D 2018
%P 402-414
%V 23
%N 123
%U http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a7/
%G ru
%F VTAMU_2018_23_123_a7
A. A. Kandakov; K. M. Chudinov. Eeffective criteria of exponential stability of autonomous difference equations. Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 402-414. http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a7/

[1] M. Marden (ed.), Geometry of Polynomials, 2nd, American Math. Soc., Providence, 1966, 243 pp. | MR

[2] J. M. McNamee, V. Pan, Numerical Methods for Roots of Polynomials, Studies in Computational Mathematics, 16, Elsevier Science, Cambridge, 2013, 718 pp. | MR

[3] S. Elaydi, An Introduction to Difference Equations, Springer, New York, 2005, 539 pp. | MR

[4] S. Levin, R. May, “A note on difference-delay equations”, Theoret. Popul. Biol., 9 (1976), 178–187 | DOI | MR

[5] I. S. Levitskaya, “A note on the stability oval for $x_{n+1}=x_n+Ax_{n-k}$”, J. Difference Equ. Appl., 11:8 (2004), 701–705 | DOI | MR

[6] F. M. Dannan, “The asymptotic stability of $x(n + k) + ax(n) + bx(n - l) = 0$”, J. Difference Equ. Appl., 7:6 (2004), 589–599 | DOI | MR

[7] M. M. Kipnis, R. M. Nigmatulin, “Stability of the trinomial linear difference equations with two delays”, Automation and Remote Control, 2004, no. 11, 25–39 (In Russian)

[8] Yu. P. Nikolaev, “The geometry of $D$-decomposition of a two-dimensional plane of arbitrary coefficients of the characteristic polynomial of a discrete system”, Automation and Remote Control, 2004, no. 12, 49–61 (In Russian)

[9] J. Čermák, J. Jánský, “Explicit stability conditions for a linear trinomial delay difference equation”, Appl. Math. Letters, 43 (2015), 56–60 | DOI | MR

[10] M. M. Kipnis, V. V. Malygina, “The stability cone for a matrix delay difference equation”, International Journal of Mathematics and Mathematical Sciences, 2011, 1–15 | DOI | MR

[11] S. A. Ivanov, M. M. Kipnis, V. V. Malygina, “The stability cone for a difference matrix equation with two delays”, ISRN Applied Math., 2011, no. 2011, 1–19 | DOI | MR

[12] A. A. Kandakov, K. M. Chudinov, “Effective stability criterion for a discrete dynamical system”, Applied Mathematics and Control Sciences, 2017, no. 4, 88–103 (In Russian)

[13] I. Schur, “Über Potenzreihen, die im Innern des Einheitkreises beschränkt sind”, J. Reine Angew. Math., 148 (1918), 122–145 | MR

[14] A. Cohn, “Über die Anzahl der Wurzein einer algebraischen Gleichung in einem Kreise”, Math. Zeit., 14 (1922), 111–148 | DOI | MR