Graphical interpretation of observability in terms of feedback circuits

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Abstract
It is known that the observability of a system depends crucially on the choice of the observable. Locally, such a feature results directly from the couplings between the dynamical variables (globally, it will also depend on symmetry). Using a feedback circuit description, it is shown how the location of the nonlinearity can affect the observability of a system. A graphical interpretation is introduced to determine—without any computation—whether a variable provides full observability of the system or not. Up to a certain degree of accuracy, this graphical interpretation allows us to rank the variables from the best to the worst. In addition to that, it is shown that provided that the system is observable, it can be rewritten under the form of a jerk system. The Rössler system and nine simple Sprott systems, having two fixed points, are investigated here.

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