In control systems, when the state equations are unknown, the design of a state observer usually consists first in identifying the model of the system from experimental data, and then in designing an observer from the identified model. This two-step procedure is generally not optimal. In this thesis, a one-step procedure is presented, where observers are directly designed from experimental data, using neural networks to approximate the nonlinearities in the system. This procedure is here used in two different applications. First, some uncertain linear systems are taken as case studies from research papers where robust linear filters are presented; a nonlinear observer is designed from data and its robustness is compared to those filters.