Cross Gramian
In control theory, the cross Gramian is a Gramian matrix used to determine how controllable and observable a linear system is. For the stable time-invariant linear system the cross Gramian is defined as: and thus also given by the solution to the Sylvester equation: The triple is controllable and observable if and only if the matrix is nonsingular, (i.e. has full rank, for any ). If the associated system is furthermore symmetric, such that there exists a transformation with then the absolute value of the eigenvalues of the cross Gramian equal Hankel singular values:
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Cross Gramian
In control theory, the cross Gramian is a Gramian matrix used to determine how controllable and observable a linear system is. For the stable time-invariant linear system the cross Gramian is defined as: and thus also given by the solution to the Sylvester equation: The triple is controllable and observable if and only if the matrix is nonsingular, (i.e. has full rank, for any ). If the associated system is furthermore symmetric, such that there exists a transformation with then the absolute value of the eigenvalues of the cross Gramian equal Hankel singular values:
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In control theory, the cross G ...... pposed to balanced truncation.
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في نظرية التحكم، معادلة جرايما ...... اتية والمتجهات الذاتية تساوي :
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In control theory, the cross G ...... equal Hankel singular values:
@en
في نظرية التحكم، معادلة جرايما ...... اتية والمتجهات الذاتية تساوي :
@ar
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Cross Gramian
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معادلة جرايمان
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