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Bilinearization up to output injection. (English) Zbl 0648.93024
Nonlinear analytic single-input single-output systems of the form \[ (\Sigma)\quad x'=Z_ 1(x)+u Z_ 2(x);\quad y=h(x) \] are considered. The authors investigate the existence of a local change of coordinates \(z=T(x)\), \(T(0)=0\), transforming (\(\Sigma)\) to

\[ (\Sigma ')\quad z'=Az+u Bz+\Phi (u,y);\quad y=Cz. \] Necessary and sufficient conditions are given for systems which are observable (in the sense of the rank condition).
Reviewer: A.Bacciotti

MSC:
93C10 Nonlinear systems in control theory
93B17 Transformations
93C15 Control/observation systems governed by ordinary differential equations
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