Invertible linear ordinary differential operators and their generalizations

In this paper, the previously obtained description of invertible linear ordinary differential operators is generalized to invertible linear discrete-time operators, unimodular matrices, and transformations of control systems. The description is based on assigning a model in the form of a set of squares on the plane to each generalized invertible operator. The number of squares of the model is invariant and can be used to classify generalized invertible operators and, in particular, transformations of control systems. (C) 2020 Elsevier B.V. All rights reserved.