Testing Generic Strong Accessibility of Nonlinear Control Systems via Polynomial (Quadratic) Immersion

Following our previous result on generic strongaccessibility (GSA) for nonlinear systems, where we showedthat GSA can be checked through a rank test on a 'nonlinearcontrollability matrix', we show here that the same test can bemade further more efficient through a preliminary polynomialsystem immersion, which is in fact always quadratic and forwhich we give here a geometric interpretation, that allows totake advantage of polynomial algebra algorithms.