Various implementations of implementable transfer matrices

An overall transfer matrix
G_{f}(s)
is said to be implementable for a given plant
G(s)
if the resulting system uses only proper compensators, has all forward paths passing through the plant, is well posed, and totally stable. A necessary condition for an overall transfer matrix to be implementable is established. The sufficiency of the condition is established by constructing several implementations. The open-loop, unity-feedback, two-input one-output compensator and plant input-output feedback configurations are used. The implementations either extend or improve the existing results.