Transfer function conditions for stabilizability

For the linear time invariant system
\bigl[\matrix {y_{c}(s)\cr y_{m}(s)}\bigr] = \bigl[\matrix{G(s)&H(s)\cr M(s)&N(s)} \bigr] \bigl[\matrix {u_{c}(s)\cr u_{r}(s)}\bigr]
a necessary and sufficient condition based on the proper rational transfer function matrices
\{G, H, M, N\}
is given for the existence of a proper stabilizing controller
u_{c}(s) = C(s)y_{m}(s)
. The condition states that the McMillan degrees of
M^{+}(s)
and
\bigl[\matrix{G^{+}(s)&H^{+}(s)\cr M{+}(s)&N{+}(s)}\bigr]
must be equal, where
\{G^{+}(s), H^{+}(s), M^{+}(s), N^{+}(s)\}
represents the unstable components of the partial fraction expansions of
\{G(s), H(s), M(s), N(s)\}
.