  In this article we focus our attention on the relation between a singular
linear discrete time system and a singular linear system of fractional nabla
difference equations whose coefficients are square constant matrices. By using
matrix pencil theory, first we give necessary and sufficient condition to
obtain a unique solution for the continuous time model. After by assuming that
the input vector changes only at equally space sampling instants, we shall
derive the corresponding discrete time state equation which yield the values of
the solutions of the continuous time model which will connect the initial
system to the singular linear system of fractional nabla difference equations.
