Observability Gramian
Encyclopedia
The Observability Gramian is a Gramian used in optimal control
theory to determine whether or not a linear system is observable.
For a linear system described by
The observability Gramian is given by
If and only if the matrix
is nonsingular for every 
, the pair 
is observable.
Optimal control
Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and his collaborators in the Soviet Union and Richard Bellman in the United States.-General method:Optimal...
theory to determine whether or not a linear system is observable.
For a linear system described by
The observability Gramian is given by
If and only if the matrix
is nonsingular for every , the pair is observable.