Open Access

Stability of a delay difference system

Advances in Difference Equations20062006:031409

DOI: 10.1155/ADE/2006/31409

Received: 28 January 2006

Accepted: 1 June 2006

Published: 2 August 2006


We consider the stability problem for the difference system x n = Axn-1 + Bxn-k, where A, B are real matrixes and the delay k is a positive integer. In the case A = -I, the equation is asymptotically stable if and only if all eigenvalues of the matrix B lie inside a special stability oval in the complex plane. If k is odd, then the oval is in the right half-plane, otherwise, in the left half-plane. If ||A|| + ||B|| < 1, then the equation is asymptotically stable. We derive explicit sufficient stability conditions for A I and A -I.


Authors’ Affiliations

Department of Mathematics, Chelyabinsk State Pedagogical University
Department of Mathematics, Southern Ural State University


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© M. Kipnis and D. Komissarova. 2006

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