Sliding Mode Differentiator versus Sliding Mode Observer: The Third Way for Particular Cases

This paper highlights the comparison, in terms of advantages and drawbacks, between sliding mode differentiators and sliding mode observers. Beyond the case where the signal to be derived comes from an unknown system, for which a differentiator is obviously required, the choice between a differentiator and an observer is not so simple. This is even more true considering that, in information theory, any unused information is lost information, e.g. time scale, structural properties...This issue has been addressed indirectly in Kalman filtering, where both the degree of confidence in the model and the quality of the signal are taken into account. However, this approach still relies on the availability of a model and on some assumptions of linearity. In this note, we focus on nonlinear settings and discuss several scenarios illustrating how differentiators and observers can be combined or selected to optimally exploit available information.