On the transformation of a nonlinear discrete-time input–output system into the strong row-reduced form

• Published in: Proceedings of the Estonian Academy of Sciences Vol. 65; no. 3; p. 220
• Main Authors: Bartosiewicz, Zbigniew, Belikov, Juri, Kotta, Uelle, Tonso, Maris, Wyrwas, Malgorzata
• Format: Journal Article
• Language: English
• Published: Tallinn Teaduste Akadeemia Kirjastus (Estonian Academy Publishers) 01-01-2016
• Subjects: Algorithms; Construction; Difference equations; Differential equations; Linear transformations; Mathematical analysis; Nonlinearity; Partial differential equations; Transformations
• ISSN: 1736-6046; 1736-7530
• DOI: 10.3176/proc.2016.3.02

The paper addresses the problem of the transformation of nonlinear discrete-time systems, described by implicit higher-order difference equations, into the strong row-reduced form. The motivating example illustrates the phenomenon that sometimes equations in the row-reduced form may contain higher-order shifts of output variables than the corresponding row degrees. This means that, in general, linear transformations of equations are not enough for transforming equations into the strong row-reduced form. Therefore, in this paper we study the possibility of using local nonlinear transformations to reduce the order of a system. A constructive (up to the solution of a system of partial differential equations) step-by-step algorithm is provided. It is followed by several illustrative examples.