H∞ criteria for robust actuator fault reconstruction for nonlinear systems in Takagi-Sugeno's form using sliding modes

In this paper, two criteria for robust actuator fault reconstruction with sliding mode observation for a class of uncertain nonlinear systems are derived. It is known, even though the sliding mode technique is robust against unknown but bounded uncertainties, that the quality of fault reconstruction under real conditions is not as good as assumed in the design stage. This is often due to the fact that the unmodeled dynamics and external disturbances have a greater variability and dimension as expected. Even if the dimension is known, it is formally limited by the existence condition for an exponentially stable error dynamics. Therefore, H∞ criteria are derived to obtain a threshold for the accuracy of fault reconstruction during sliding motion. The validity and applicability of the design approach is demonstrated by the inverted pendulum benchmark.