Linear Recurrence Relations and Ordinary Generating Functions Applied On Modelling Processes in Control Theory

Abstract

In this paper we apply multistep recurrence relations, as one of very simple and useful mathematical models. It is an efficient tool for solving many problems in mathematics, science, and technics. We also use generating functions, as a connection between real number sequences and real functions, and as a very smooth and efficient connection between the discrete mathematics and (continual) mathematical analysis. We present an application of multistep homogenous linear recurrence relations for modelling some processes in the control theory. Further on, we use the ordinary generating function aiming to find appropriate formulae for calculating members of an appropriate recurrence sequence. Finally, we show the application of this novel mathematical approach on one real example in the control theory.