Exponential stability results for variable delay difference equations

Abstract

Sufficient conditions that guarantee exponential decay to zero of the variable delay difference equation $x(n+1)=a(n)x(n)+b(n)x(n-g(n))$ are obtained. These sufficient conditions are deduced via inequalities by employing Lyapunov functionals. In addition, a criterion for the instability of the zero solution is established. The results in the paper generalizes some results in the literature.