We consider continuous-time LTI systems with either unknown-input or with lack of information about the input and output derivatives. We compute the unknown-input observability subspace and the observability subspace with unknown derivatives of input and output. We first formulate the unknown-input observability subspace via projection matrices, then show that through having the unknown input observability subspace, one can easily evaluate the effect of known input and output signals but unknown derivatives on the observability subspace. Our method is demonstrated on the dynamics of a longitudinal aircraft in steady-state flight.
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