A Blended Approach to Observer Discretization

This article is devoted to the discretization of continuous-time nonlinear observers for a class of systems formulated under input–output injection form.The proposed methodology focuses on improving the accuracy of the evaluation of nonlinear terms using an approximated integral formula that requires a prior prediction of the measured output. This methodology can be naturally combined with homogeneous observation error correction terms, even if the input-output injection terms are not homogeneous. Consequently, the proposed approximate integral formula can be applied to the discretization of any continuous-time observer designed for systems in input-output injection form. In the simulations, a Luenberger observer and a homogeneous observer are applied to a nonlinear controlled oscillator. The results highlight, in both cases, the superior accuracy of the proposed method.