It is common practice in state estimation of chemical systems to include augmented states modeled as random-constant or random-walk processes. When process controllers with integral terms are present, undesirable interaction effects may occur between the augmented states and the controllers. If no attention is paid to this interaction, the resulting estimator may diverge. In this work the interaction between controller and augmented states is analyzed. Using the linear systems theory, it is shown that the unwanted interaction and final divergence are caused by lack of detectability of the augmented system. A specific test, based on the Popov-Belevitch-Hautus rank test, to check the detectability in the system under study is derived. In many cases the test can be performed by simple inspection. A series of examples are given where the concept of detectability is applied to help in discovering and preventing the negative interaction between controllers and augmented states. Finally, a discussion is presented comparing the results of the standard observability test, applied to a real problem, with those obtained with the test derived here and with the behavior of a real estimator for the same problem. It is concluded that the standard observability test is not able to discriminate between different estimator designs and consequently to produce practical results as those obtained with the alternative test, i.e., the disclosure of unfeasible estimator designs.