8

Observable
Decomposition

qLet be a state space realization of a
(not necessarily stable) transfer matrix *G*(*s*). Suppose that there exists a symmetric matrix

(*Q* is not necessarily the
Gramian) with *Q**1* nonsingular such that

• Now partition the realization (*A,B,C,D*) compatibly with *Q *as

Then is also a
realization of *G.*

Moreover, (*C**1 **, A**11*) is observable if *A**11* is
stable.