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

Following our previous result on generic strong accessibility (GSA) for nonlinear systems, where we showed that GSA can be checked through a rank test on a 'nonlinear controllability matrix', we show here that the same test can be made further more efficient through a preliminary polynomial system immersion, which is in fact always quadratic and for which we give here a geometric interpretation, that allows to take advantage of polynomial algebra algorithms.