On ordinary difference equations with variable coefficients (Q1856793)

The author considers the Cauchy problem for the general ordinary linear difference equation of fixed order \(N\in\mathbb{N}\) with variable complex coefficients, solved for the sequence member with highest index. A solution representation in matrix form is given for all orders. Sufficient criteria for the asymptotic stability and the bounded input-bounded output stability of the solution sequence are presented. The solution representation is generalized to a class of partial difference equations with variable coefficients.