It is shown that under a weak observability assumption, the nonlinear Luenberger observer exists and ensures an exponential convergence rate of the estimate towards the state of the system. Moreover, it is shown that under the complete observability assumption, this class of observers is tunable. More specifically, it is shown that the estimate reaches a predetermined neighborhood of the state after a parameterizable time.
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Vincent Andrieu (2014) studied this question.
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