Observability of nonlinear state space systems - a derivation

Full derivation of nonlinear system observability condition.

The definition of observability of a linear time invariant state space system and its evaluation are well known. The observability matrix has to be full rank in order for a linear system to be observable. The derivation of the observability condition for a nonlinear state space system - which is the most commonly used formulation in the real world - is slightly more complex. This note derives the observability condition of a nonlinear system and shows its connection with the observability matrix of a linear system.

Acknowledgements to this YouTube lecture and this article (accompanying article to a Python tool box to perform observability analysis), from which I derived help for this tech note.

The derivation can be found here.