A perspective on singularity in 2D linear systems (Q1574364)

Linear multidimensional singular control systems with constant coefficients are considered. Using algebraic methods, the solution to singular difference equations with several independent variables is discussed. Special attention is paid to the so-called repetitive discrete processes and their solutions. As special cases, many different singular 2D linear control systems are discussed in detail. The relationships between various models of 2D singular systems are explained. In the proofs of the theorems, an algorithm with elementary operations and variable transforms are used. Moreover, the paper contains many remarks and comments on multidimensional discrete control systems, and relationships to results existing in the literature. Singular multidimensional control systems have been considered in many publications, e.g., in the paper of \textit{T. Kaczorek} [IEEE Trans. Autom. Control, AC-33, 1060-1061 (1988; Zbl 0655.93046)].