Bilinearization up to output injection (Q1105528)

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).