# Flat input based canonical form observers for non-integrable nonlinear systems

## DOI:

https://doi.org/10.52846/stccj.2022.2.1.31## Keywords:

nonlinear systems, observer design, observer error linearization, differential flatness, flat inputs## Abstract

In this contribution, the design of canonical form observers for nonlinear non-integrable systems is investigated. These systems cannot be transformed into observer canonical form, therefore an exact observer error linearization cannot be achieved. However, using flat inputs and dynamic compensators, the original dynamics can be rendered into an integrable flat system. For this modified flat input system a canonical form observer can be designed. By utilizing a state transformation, it is then possible to obtain an estimate of the original state, where the observer error is approximately linearized. This procedure is exemplified by the Rössler system. Furthermore, we illustrate the relationship of this approach with high-gain observers.

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*Syst. Theor. Control Comput. J.*, vol. 2, no. 1, pp. 13–21, Jun. 2022, doi: 10.52846/stccj.2022.2.1.31.