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
Famous quotes containing the word case:
“It was a maxim with Mr. Brass that the habit of paying compliments kept a man’s tongue oiled without any expense; and that, as that useful member ought never to grow rusty or creak in turning on its hinges in the case of a practitioner of the law, in whom it should be always glib and easy, he lost few opportunities of improving himself by the utterance of handsome speeches and eulogistic expressions”
—Charles Dickens (1812–1870)