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Article Dans Une Revue Mathematics of Control, Signals, and Systems Année : 2015

From exact observability to identification of singular sources

Marius Tucsnak
George Weiss
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Résumé

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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Dates et versions

hal-01278500 , version 1 (24-02-2016)

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Marius Tucsnak, George Weiss. From exact observability to identification of singular sources. Mathematics of Control, Signals, and Systems, 2015, 27 (1), pp.1-21. ⟨10.1007/s00498-014-0132-z⟩. ⟨hal-01278500⟩
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