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Effective criteria of exponential stability of autonomous difference equations


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.


difference equation; stability; stability domain; Schur–Cohn polynomial

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1. Marden M. Geometry of Polynomials. Providence, American Math. Soc., 1966, 243 p. 2. McNamee J.M., Pan V. Numerical Methods for Roots of Polynomials. Studies in Computational Mathematics. Cambridge, Elsevier Science, 2013, vol. 16, 718 p. 3. Elaydi S. An Introduction to Difference Equations. New York, Springer, 2005, 539 p. 4. Levin S., May R. A note on difference-delay equations. Theoret. Popul. Biol., 1976, vol. 9, pp. 178-187. 5. Levitskaya I.S. A note on the stability oval for xn+1 = xn +Axn􀀀k: J. Difference Equ. Appl., 2004, vol. 11, no. 8, pp. 701-705. 6. Dannan F.M. The asymptotic stability of x(n+k)+ax(n)+bx(n−l) = 0: J. Difference Equ. Appl., 2004, vol. 7, no. 6, pp. 589-599. 7. Kipnis M.M., Nigmatulin R.M. Ustoychivost’ trekhchlennykh lineynykh raznostnykh uravneniy s dvumya zapazdyvaniyami [Stability of the trinomial linear difference equations with two delays]. Avtomatika i telemekhanika – Automation and Remote Control, 2004, no. 11, pp. 25-39. (In Russian). 8. Nikolaev Yu.P. Analiz geometrii D-razbieniya dvumernoy ploskosti proizvol’nykh koehffitsientov kharakteristicheskogo polinoma diskretnoy sistemy [The geometry of D-decomposition of a two-dimensional plane of arbitrary coefficients of the characteristic polynomial of a discrete system]. Avtomatika i telemekhanika – Automation and Remote Control, 2004, no. 12, pp. 49-61. (In Russian). 9. Čermák J., Jánský J. Explicit stability conditions for a linear trinomial delay difference equation. Appl. Math. Letters, 2015, vol. 43, pp. 56-60. 10. Kipnis M.M., Malygina V.V. The stability cone for a matrix delay difference equation. International Journal of Mathematics and Mathematical Sciences, 2011. Article ID 860326, 15 p. 11. Ivanov S.A., Kipnis M.M., V.V. Malygina V.V. The stability cone for a difference matrix equation with two delays. ISRN Applied Math., 2011, no. 2011, pp. 1-19. 12. Kandakov A.A., Chudinov K.M. Ehffektivnyy kriteriy ustoychivosti diskretnoy dinamicheskoy sistemy [Effective stability criterion for a discrete dynamical system]. Prikladnaya matematika i voprosy upravleniya – Applied Mathematics and Control Sciences, 2017, no. 4, pp. 88-103. (In Russian). 13. Schur I. Über Potenzreihen, die im Innern des Einheitkreises beschr¨ankt sind. J. Reine Angew. Math., 1918, vol. 148, pp. 122-145. (In German). 14. Cohn A. Über die Anzahl der Wurzein einer algebraischen Gleichung in einem Kreise. Math. Zeit., 1922, vol. 14, pp. 111-148. (In German).



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