Solution of weakly delayed linear two-dimensional discrete systems with constant coefficients and multiple delays

Abstract

A solution of weakly delayed two-dimensional linear discrete systems with constant coefficients and multiple delays x(k+1)=Ax(k)+∑l=1nBlx(k−ml),k≥0 is presented. In the system, n and mi, i = 1, …, n are positive integers, m1 < m2 < … <mn, A, Bi, i = 1, …, n are nonzero 2 × 2 constant matrices and x:{−mn,…,∞}→ℝ2 is a solution. Formulas for general solutions are derived. For k ≥ mn, these general solutions can also be derived by transforming general solutions of certain linear systems without delays.