We consider smooth single-input, two-output systems on a compact manifold X. We show that the set of systems that are observable for any polynomial input whose degree is less than or equal to a given bound contains an open and dense subset of the set of smooth systems.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am28-3-4, author = {Philippe Jouan}, title = {Observability of control systems for polynomial inputs and genericity}, journal = {Applicationes Mathematicae}, volume = {28}, year = {2001}, pages = {281-291}, zbl = {1016.93011}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-3-4} }
Philippe Jouan. Observability of control systems for polynomial inputs and genericity. Applicationes Mathematicae, Tome 28 (2001) pp. 281-291. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-3-4/