Stability in discrete equations with variable delays

Abstract

In this paper we study the stability of the zero solution of difference equations with variable delays. In particular we consider the scalar delay equation \begin{equation} \Delta x(n)=-a(n)x(n-\tau(n)) \end{equation} and its generalization \begin{equation} \Delta x(n)=-\sum^{N}_{j=1}a_j(n)x(n-\tau_j(n)). \end{equation} Fixed point theorems are used in the analysis.