On the Use of the Time-Integrals of the Output in Observer Design for Nonlinear Autonomous Systems

The goal of this article is to show that the observation scheme recently proposed for linear systems by Menini et al. in 2019, achieving good performance in the presence of a high-frequency measurement disturbance, can be adapted to be used for nonlinear autonomous systems. The design is based on the use of the time-integrals of the measured output and requires the availability of a state observer able to provide a rough estimate of the state; the proposed scheme can be then understood as an observer postprocessing algorithm. For the implementation of the proposed scheme, the time-integrals of the output are required to express as functions of the state of the system. Such functions are called directional antiderivatives; in the article, conditions to guarantee their existence and methods for their computation, in closed-form or by approximation, are resumed. The performance of the proposed observation scheme is illustrated through an example.