Nonlinear Case
Given the system, . Where the state vector, the input vector and the output vector. are to be smooth vectorfields.
Now define the observation space to be the space containing all repeated Lie derivatives. Now the system is observable in if and only if .
Note:
Early criteria for observability in nonlinear dynamic systems were discovered by Griffith and Kumar, Kou, Elliot and Tarn, and Singh.
Read more about this topic: Observability
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