Given G(s), find (A,B,C,D) such that
which is a state space realization of G(s).
A state space realization (A,B,C,D) of G(s) is minimal if and only if (A,B) is controllable and (C,A) is observable.
Let (A1,B1,C1,D) and (A2,B2,C2,D) be two minimal realizations of G(s). Then there exists a unique
nonsingular T such that
A2=TA1T-1, B2=TB1, C2=C1T-1.
Furthermore, T can be specified as
T=(O2*O2)-1O2*O1 or T-1=C1C2*(C2C2*)-1.
where C1, C2, O1, and O2 are the
corresponding controllability and observability matrices respectively.