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From exact observability to identification of singular sources

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Abstract

We give general results about the identifiability of source terms for infinite-dimensional linear systems that are exactly observable. We allow the source term to be unbounded, i.e., not contained in the state space, but in one of a sequence of extended spaces. We show that the operator from the source term to the output function is bounded from below, in suitable norms. We apply the main result to a system described by the wave equation in a bounded \(n\)-dimensional domain. We derive results of independent interest concerning the range of the input map of an exactly controllable system, when restricted to various spaces of smooth input functions.

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Authors and Affiliations

  1. Institut Elie Cartan, Université de Lorraine, 54506 , Vandoeuvre-lés-Nancy, France

    Marius Tucsnak

  2. Department of EE-Systems, Tel Aviv University, 69978 , Ramat Aviv, Israel

    George Weiss

Authors
  1. Marius Tucsnak
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  2. George Weiss
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Correspondence to Marius Tucsnak.

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Tucsnak, M., Weiss, G. From exact observability to identification of singular sources. Math. Control Signals Syst. 27, 1–21 (2015). https://doi.org/10.1007/s00498-014-0132-z

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  • DOI: https://doi.org/10.1007/s00498-014-0132-z

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