Abstract
A universal input is an inputu with the property that, whenever two states give rise to a different output for some input, then they give rise to a different output foru. For an observable system,u is universal if the initial state can be reconstructed from the knowledge of the output foru. It is shown that, for continuous-time analytic systems, analytic universal inputs exist, and that, in the class ofC ∞ inputs, universality is a generic property. Stronger results are proved for polynomial systems.
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Sussmann, H.J. Single-input observability of continuous-time systems. Math. Systems Theory 12, 371–393 (1978). https://doi.org/10.1007/BF01776584
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DOI: https://doi.org/10.1007/BF01776584