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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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