qLet be a state space realization of a
(not necessarily stable) transfer matrix G(s). Suppose that there exists a symmetric matrix
q
• (Q is not necessarily the
Gramian) with Q1 nonsingular such that
• A*Q+QA+C*C=0
• Now partition the realization (A,B,C,D) compatibly with Q as
•
•
• Then is also a
realization of G.
• Moreover, (C1 , A11) is observable if A11 is
stable.