From exact observability to identification of singular sources

Marius Tucsnak, George Weiss

Research output: Contribution to journalArticlepeer-review


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 (Formula presented.)-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.

Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalMathematics of Control, Signals, and Systems
Issue number1
StatePublished - Mar 2014


  • Exact controllability
  • Exact observability
  • Inverse problems
  • Point sources
  • Wave equation

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Signal Processing
  • Control and Optimization
  • Applied Mathematics


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