Stability of certain distributed parameter systems by low dimensional controllers: a root locus approach

The authors consider a root locus approach to enhance stability for a special class of one-dimensional distributed parameter systems using low-dimensional boundary controllers. It is shown that when there are lower order noncolocated terms in the boundary conditions, the problem is not self-adjoint and the open loop system is unstable. Since the zero dynamics is stable the corollary considered implies that the system can be stabilized by introducing the simple PI (proportional plus integral) feedback law and tuning the gain