Eeffective criteria of exponential stability of autonomous difference equations
Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 402-414

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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.
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/
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[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