Observability Gramian

The Observability Gramian is a Gramian used in control theory to determine whether or not a linear system is observable.

For a linear system described by

The observability Gramian for a linear time variant system is given by

,

where is the state transition matrix.

The system is observable on the interval if and only if is nonsingular. In the case of a linear time invariant system, this can be simplified to finding the rank of the "observability matrix". If is a -dimensional real-valued vector, then the system is observable if and only if

See also

External links


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