If you cancel the (s-3) term, then G(s) is in its lowest term (the num
and the den are co-primes polynomials), and hence it has only a
minimal realization, hence by definition the realization is both
controllable and observable. Hence there is no uncontrollable
If you do not do any cancellation, then you can use the
controllability structure theory to convert this into a controllable
and uncontrollable parts. Use similarity transformation
Abar=T*A*inv(T). Need to find T, which is obtained from the
The new A matrix will be in the form [A11 A12;0 A22]. and the B matrix
will be [B1;0]. In this (A11,B1) is the controllable system, and A22
is the uncontrollable part.
If you have matlab, do help on the function ctrbf, this will do all
the work for you.
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