Kybernetika 54 no. 4, 736-747, 2018

Realization of nonlinear input-output equations in controller canonical form

Arvo Kaldmäe and Ülle KottaDOI: 10.14736/kyb-2018-4-0736


In this paper necessary and sufficient conditions are given which guarantee that there exists a realization of a set of nonlinear higher order differential input-output equations in the controller canonical form. Two cases are studied, corresponding respectively to linear and nonlinear output functions. The conditions are formulated in terms of certain sequence of vector spaces of differential 1-forms. The proofs suggest how to construct the transformations, necessary to obtain the specific state space realizations. Multiple examples are added, which describe different scenarios.


nonlinear systems, realization, algebraic methods


93B11, 93C10, 93B25


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