Geodesic
An asymptotic expansion of the solution of a~matrix difference equation of general form
Sbornik. Mathematics, Tome 205 (2014) no. 12, pp. 1815-1828

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An asymptotic expansion of the solution of an inhomogeneous matrix difference equation of general form is obtained. The case when there is no bound on the differences of the arguments is considered. The effect of the roots of the characteristic equation is taken into account. An integral estimate with a submultiplicative weight is established for the remainder in terms of the submultiplicative moment of the free term of the equation. Bibliography: 14 titles.
Keywords: matrix difference equation, unbounded delay, characteristic equation, submultiplicative function, asymptotic behaviour, Banach algebra. 
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     author = {M. S. Sgibnev},
     title = {An asymptotic expansion of the solution of a~matrix difference equation of general form},
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M. S. Sgibnev. An asymptotic expansion of the solution of a~matrix difference equation of general form. Sbornik. Mathematics, Tome 205 (2014) no. 12, pp. 1815-1828. http://geodesic.mathdoc.fr/item/SM_2014_205_12_a7/