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2.11 Linear Controller Design 97

then

Therefore, this system is controllable but not observable. On the other hand,
the system

then

so this one is observable but not controllable. The trouble is that both of
-1
these realizations have the same transfer function H(s)=c(sI-A) b= s/s =s!.
2

Suppose we have 2 realizations of the transfer function H(s) related by a
state-space transformation,

(2.11.6)

and

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