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On the transformation of a nonlinear discrete-time input–output system into the strong row-reduced form; pp. 220–236

Full article in PDF format | doi: 10.3176/proc.2016.3.02

Zbigniew Bartosiewicz, Juri Belikov, Ülle Kotta, Maris Tõnso, Małgorzata Wyrwas


The paper addresses the problem of the transformation of nonlinear discrete-time systems, described by implicit higherorder 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.



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