
438
J.A. Ramos and E.L Verriest
3 BALANCED REALIZATIONS
Here we will show that the orthogonal complement matrices Np and
N!
satisfy certain
constraints that lead to the balanced conditions similarly derived in [7]. First, let us point
out that Np and
N!
satisfy the following system of equations
Now. since the two systems of equations are equivalent, one needs to solve only one system.
Let [
T, IT4 ]= [ NTI-NT
],
then from (22) we have
T2r + T4rA ~ = 0~•
(24)
T1 + T2HT
+ T4EA = 0~i• (25)
T3 + T4HT
= 0tixmi (26)
Since the product r& is similarity invariant, one can specify a similarity transformation ...