Abstract
Using the geometric approach, a solution is given to the problem of detecting faults in linear periodic discrete-time systems. The solution consists on developing an unknown input observer. The existing conditions are provided in terms of new geometric notion of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">outer</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">observable</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">subspace</i> that is the dual notion of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">inner</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">reachable</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">subspace</i> . Making use of the new notion, a residual generator is developed, such that the residual is made independent of unknown input disturbance, and its output-free response goes asymptotically to zero.
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