The concept of observer-based compensators (OBCs) and the deterministic separation principle have long been cornerstones of modern control theory. In our paper, we extend these ideas via singular system theory to encompass a wider variety of rational compensators. We show that the separation principle generalizes in a natural way to OBCs of all orders, including the static case. We pay particular attention to the problems of properness and conjugate symmetry. Our intention is to provide an introductory account of this framework and to suggest possible avenues of further development.