As discussed in [452, p. 362] and exemplified in §C.17.6, to diagonalize a system, we must find the eigenvectors of by solving

for , , where is simply the th pole (eigenvalue of ). The eigenvectors are collected into a

If there are coupled repeated poles, the corresponding missing eigenvectors can be replaced by generalized eigenvectors.

The new diagonalized system is then

(2.13) |

where

The transformed system describes the same system as in Eq. (1.8) relative to new state-variable coordinates . For example, it can be checked that the transfer-function matrix is unchanged.

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