For a delay difference equation x(n + 1) = ∑k=-dn A(n, k)x(k) + f(n) in a Banach space the following result is proved: if for any f ∈ lp the solution is x ∈ lp then the solution of the homogeneous equation (f ≡ 0) is exponentially stable. This result is applied to obtain new explicit conditions for exponential stability of a scalar nonautonomous delay difference equation.
- Difference equations
- Explicit stability conditions
- Exponential dichotomy
- Exponential stability