Root-Locus Theory for Infinite-Dimensional Systems

In this thesis, the root-locus theory for a class of diffusion systems is studied. The input and output boundary operators are co-located in the sense that their highest order derivatives occur at the same endpoint. It is shown that infinitely many root-locus branches lie on the negative real axis and the remaining finitely many root-locus branches lie inside a fixed closed contour. It is also shown that all closed-loop poles vary continuously as the feedback gain varies from zero to infinity