## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 566-571 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

DOIs | |

State | Published - 1978 |

Event | Proc IEEE Conf Decis Control Incl Symp Adapt Processes 17th - San Diego, CA, USA Duration: Jan 10 1979 → Jan 12 1979 |

## All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization