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

Diskreetsete mittelineaarsete sisend-valjundvorrandite teisendamine tugevale reapohiselt taandatud kujule

Zbigniew Bartosiewicz ； Juri Belikov ； Ulle Kotta ； Maris Tonso ； Malgorzata Wyrwas

《Proceedings of the Estonian Academy of Sciences》 65卷3期 (2016/09) Pp. 220-236

https://doi.org/10.3176/proc.2016.3.02

並列摘要

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.

並列關鍵字

discrete-time systems ； input-output models ； input-output equivalence transformations ； strong row-reduced form