This paper focuses on a new kind of artificial neural networks - the Z-transform artificial neural networks (ZTANNs). It is proposed to use the Z-transform instead of ordinary weights and a linear activation function of an artificial neuron. This extension allows to use artificial neural networks in new areas. The ordinary description of artificial neural networks is a special case of the description proposed in this paper. It also contains a description of the use of the ZTANN for automatic identification of objects in digital control system. (C) 2015 Elsevier B.V. All rights reserved.