A new approach to the Z-transform through infinite computation

The Z-transform is an important mathematical tool to model sample-data control systems or other discrete-data systems. Since the Z-transform is defined as sum of an infinite number of addends, it is very interesting to look at it from non-classical points of view through one of the many current theories that today provide a wide range of different infinities and infinitesimals. In this paper, therefore, we choose to adopt a new simple applied approach recently proposed by Y.D. Sergeyev that allows one to execute easily numerical computations with various sizes of infinite and infinitesimal numbers. Using this new approach, we obtain a very different type of Z-transform of a complex sequence (or better, a family of infinitely many Z-transforms attached to the same sequence) whose existence is guaranteed almost everywhere on C, unlike what happens in traditional analysis in which the bilateral Z-transform often does not exist anywhere. (C) 2019 Elsevier B.V. All rights reserved.