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To diagonalize our force-driven mass example, we may begin with its
state-space model Eq.(1.9):
which is in the general state-space form
as needed (Eq.(1.8)). We can see that
is already a
Jordan block of order 2 [452, p. 368]. (We can change the
to 1 by scaling the physical units of
.) Thus, the system
is already as diagonal as it's going to get. We have a repeated pole
at
, and they are effectively in series (instead of parallel),
thus giving a ``defective''
matrix [452, p. 136].
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