Generic single-input observability of continuous-time polynomial systems

It is shown that, for observable continuous time systems Whose dynamics and output are given by polynomial functions, the observation of the output that corresponds to a single input u is sufficient to determine the initial state, provided that u is suitably chosen. The "good" u\´s are an open dense subset of the set of all infinitely differentiable inputs. In particular, one can choose u to be a polynomial. Moreover, if the degree N is sufficiently large, then the "good" polynomial inputs of degree not greater than N form an open dense subset W of the set of all polynomials of degree not greater than N. The set W is semialgebraic, i.e., describable by finitely many polynomial inequalities. Similar results are proved for parameter identification.