On ordinary difference equations with variable coefficients

A solution representation in matrix form is achieved for all orders of the title equation. Sufficient criteria for the asymptotical stability and the bounded input–bounded output stability of the solution sequence are presented. Our solution representation is confronted with a fully explicit representation. The latter is derived in a simple way and also generalized to a class of partial difference equation with variable coefficients.  2002 Elsevier Science (USA). All rights reserved.