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Transfer equivalence and realization of nonlinear higher order input/output difference equations using Mathematica

Ülle Kotta
Organization: Tallinn Technical University
Department: Institute of Cybernetics
Maris Tõnso
Organization: Tallinn Technical University
Department: Institute of Cybernetics
Journal / Anthology

Journal of Circuits, Systems, and Computers
Year: 1999
Volume: 9
Issue: 1-2
Page range: 23-35

this paper presents a contribution to the development of symbolic computation tools for discrete-time nonlinear control systems. A set of functions is developed in Mathematica 3.0 that test if the higher order input/output difference equation is realizable in the classical state-space form, and for simple examples, also find such state equations. The approach relies on a new notion of equivalence of higher-order difference equations which yields a minimal (i.e. accessible and observable) realization and generalizes the notion of transfer equivalence to the nonlinear case. The application of the developed functions is demonstrated on three examples obtained via identification.

*Engineering > Control Theory