The non-integer difference of the discrete-time function and its application to the control system synthesis

A definition of a non-integer nth order backward difference of the discrete-time function is given. It is a generalization of the well-known nth order difference, where n is a positive integer. Some simple examples of the non-integer nth order differences of several fundamental functions are given. The application of the nth order difference in the closed-loop discrete-time systems control algorithms are illustrated by numerical examples.