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Process Control: Modeling, Design, and Simulation by B. Wayne Bequette

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M13.6. Singular Value Analysis

The SVD can be used to predict directional sensitivity of a process. The process gain matrix is decomposed into three matrices,

where U is the left singular vector matrix, Σ the diagonal matrix of singular values, ordered, and V the right singular vector matrix. The left and right singular vector matrices are both orthonormal matrices; that is, each column of the matrix is orthogonal to all other columns and the columns each are unit length. The diagonal singular value matrix is ordered so that the largest singular value is in the (1,1) position. Note that the standard notation for SVD is to use U to represent the ...

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