Stability of a time discrete perturbed dynamical system with delay

Michael I. Gil' and Sui Sun Cheng

Discrete Dynamics in Nature and Society, 1999, vol. 3, 1-7

Abstract:

Let C n be the set of n complex vectors endowed with a norm ‖ ⋅ ‖ C n . Let A , B be two complex n × n matrices and τ a positive integer. In the present paper we consider the nonlinear difference equation with delay of the type u k + 1 = A u k + B u k − τ + F k ( u k , u k − τ ) , k = 0 , 1 , 2 , … , where F k : C n × C n → C n satisfies the condition ‖ F k ( x , y ) ‖ C n ≤ p ‖ x ‖ C n + q ‖ y ‖ C n , k = 0 , 1 , 2 , … , where p and q are positive constants. In this paper, absolute stability conditions for this equation are established.

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:317646

DOI: 10.1155/S1026022699000084

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