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- Controllability_Gramian abstract "In control theory, the controllability Gramian is a Gramian used to determine whether or not a linear system is controllable.For the time-invariant linear system if all eigenvalues of have negative real part, then the unique solution of the Lyapunov equationis positive definite if and only if the pair is controllable. is known as the controllability Gramian and can also be expressed asA related matrix used for determining controllability isThe pair is controllable if and only if the matrix is nonsingular, for any . A physical interpretation of the controllability Gramian is that if the input to the system is white gaussian noise, then is the covariance of the state.Linear time-variant state space models of form ,are controllable in an interval if and only if the rows of the matrix product where is the state transition matrix are linearly independent.The Gramian is used to prove the linear independency of .To have linear independency Gramian matrix have to be nonsingular, i.e., invertible.".
- Controllability_Gramian wikiPageExternalLink ControllabilityGramian.html.
- Controllability_Gramian wikiPageID "5347320".
- Controllability_Gramian wikiPageRevisionID "577488783".
- Controllability_Gramian hasPhotoCollection Controllability_Gramian.
- Controllability_Gramian subject Category:Control_theory.
- Controllability_Gramian comment "In control theory, the controllability Gramian is a Gramian used to determine whether or not a linear system is controllable.For the time-invariant linear system if all eigenvalues of have negative real part, then the unique solution of the Lyapunov equationis positive definite if and only if the pair is controllable.".
- Controllability_Gramian label "Controllability Gramian".
- Controllability_Gramian label "Matrice gramiana di controllabilità".
- Controllability_Gramian sameAs Matrice_gramiana_di_controllabilità.
- Controllability_Gramian sameAs m.0dgqg5.
- Controllability_Gramian sameAs Q83587.
- Controllability_Gramian sameAs Q83587.
- Controllability_Gramian wasDerivedFrom Controllability_Gramian?oldid=577488783.
- Controllability_Gramian isPrimaryTopicOf Controllability_Gramian.