Reducing the error of sampled-data nonlinear observers with numerical approaches

The problem of how to reduce the error of sampled-data nonlinear observers is investigated. A two-step design approach is proposed, in which the feedback term of observer is designed in continuous-time while an accurate numerical approach is used to estimate the state at next sampling instance. Main theorem is proved to guarantee that the observer error decays to and remains in a bounded ball contains the origin and the bound can be controlled by the numerical approach. Compared with approximate discrete-time design method, the two-step approach can have the same observer precision while the design is relatively easy because the continuous-time design methods can be used directly.