Here, &jnkij(s) and n ..(s) denote the numerator
polynomials of kij(s) an%&ij(s), while dk(S) and d (s)
are the denominator polynomials. Finally, note b a t
~ ( sa)nd @(s)a re the transmission zero and characteristic
polynomials for the open-loop system K(s)G(s), and
~ ( s c)a n be split into compensator and plant
transmission zero polynomials, vk(s) and wg(s).
From Eq. (3, note a two-channel feedback system
results in a 2 d order polynomial relationship in k
governing the closed-loop poles, rather than a linear
relationship associated with scalar-loop feedback
systems. Further, there are now two open-loop
"numerator" polynomials which determine the loci
behavior: ~ ( sa)nd fls), which depend on the individual
open-loop numerator polynomials. Eq. (5) can also be
interpreted as