Bilinearization up to output injection. (English) Zbl 0648.93024

Hammouri, H.; Gauthier, J. P.

Syst. Control Lett. 11, No. 2, 139-149 (1988).

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

Keywords:

output injection; bilinear systems; bilinearization; Nonlinear analytic single-input single-output systems

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