An on-line state-estimation design for multiinput multioutput nonlinear plants, either observable or detectable, is presented The design considers a stage of analysis, in which the solvability of the estimation problem with robust convergence is assessed a priori, and a stage of synthesis, in which the estimator is constructed and its gains are tuned with a systematized procedure. The approach, which stems from a suitable definition of robust nonlinear observability or detectability, provides a methodological framework that identifies the compromise between the performance and the robustness of the estimator and interprets the functioning of the estimator with notions and vocabulary from conventional-type linear filtering and control techniques. The problem for a class of free-radical homopolymerization reactors is studied as an application example showing how the proposed design, together with available nonlinear dynamics modeling and characterization methods, can be applied to polymer reactor engineering in particular and to chemical-process engineering in general.