Single-input observability of continuous-time systems

A universal input is an input u with the property that, whenever two states give rise to a different output for some input, then they give rise to a different output for u. For an observable system, u is universal if the initial state can be reconstructed from the knowledge of the output for u. It is shown that, for continuous-time analytic systems, analytic universal inputs exist, and that, in the class of C^∞ inputs, universality is a generic property. Stronger results are proved for polynomial systems.