Branches Passing Through Infinity in the Root Locus Method

In this paper, construction rules of the root locus of a
positive feedback system whose loop transfer function is
not strictly proper have been investigated.
The root locus method is being used since 1950. It is
demonstrated that some of the steps in this technique are
not general and for a positive feedback system whose
loop transfer function is not strictly proper are not valid.
To overcome this problem, new definitions for root
locus branches have been presented which divide them
into branches passing through infinity and branches
ending/starting at/from infinity.
We have also considered the realization and stability of these systems.