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Observability is a key property of dynamic systems, which deals with the question of whether the state of a system can be uniquely determined in a finite time interval from inputs and measured outputs provided that the system dynamic model is known:

 For linear systems, observability is a global property and there is a universal definition for it. An LTI (LTV) system is observable, if and only if its observability matrix (observability Gramian matrix) is full‐rank, and the state can be reconstructed from inputs and measured outputs using the inverse of the observability matrix (observability Gramian matrix).

 For nonlinear systems, a unique definition of observability does not exist and locally weak observability is considered in a neighborhood of the initial state. A nonlinear system is locally weakly observable if its Jacobian matrix about that particular state has full rank. Then, the initial state can be reconstructed from inputs and measured outputs using the inverse of the Jacobian.

 For stochastic systems, mutual information between states and outputs can be used as a measure for the degree of observability, which helps to reconfigure the sensory (perceptual) part of the system in a way to improve the observability [33].