I. Introduction
In the context of engineering sciences, motivations to study continuous-time difference equations come from sampled-data systems, neutral time-delay systems (see [1], [2], and [3]), difference equations with distributed delays (see examples in [4]), conservation laws modeled by first-order hyperbolic partial differential equations in which a transport phenomenon occurs [2], and other classes of linear systems with distributed parameters, which have been shown in [5] to admit such a representation. Physical examples of these systems include wave equations (a particular case of hyperbolic partial differential equations), whose applications range from acoustics, electrical engineering (e.g., the telegraph equation in [6]), to mechanics and communications.