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INPUT-OUTPUT EQUIVALENCE OF NONLINEAR SYSTEMS AND THEIR REALIZATIONS
Claude H. Moog* Yufan Zheng** Pin Liu***
* Institut de Recher che en Communications et Cybernétique de
Nantes, 1 rue de la Noë, BP 92101, 44321 Nantes Cedex 3,
France. E-mail: moog@irccyn.ec-nantes.fr
** Department of Electrical and Electronic engineering, The
University of Melbourne, Vic 3010, Australia.
E-mail:y.zheng@eemuozau.
*** Marconi Communications Ltd, Discovery Court, 551/3 Wallis
Down Road, Poole, Dorset BH12 5AG, UK. E-mail:
Pin.Liu@marconic omms.om
The notion of realization for single-input single-output nonlinear systems is studied based on a new notion of input-output equivalence. This equivalence relation aims to generalize the equivalence of linear time-invariant systems in the sense of the equality of their transfer functions. Necessary and sufficient conditions are given for the existence of a realization, affine or not. A minimal (i.e. accessible and observable) realization may then be derived for those systems which satisfy these conditions, after seeking an equivalent reduced order input-output system.
Keywords: Nonlinear systems, realization, equivalence, algebraic methods
Session slot T-Mo-M08: Analysis of Nonlinear Systems/Area code 2c : Non-linear Systems
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