Robust sensitive fault detection and estimation for single-rate and multirate nonlinear sampled-data systems

This paper investigates the problem of fault detection and estimation for nonlinear sampled-data systems in the presence of unknown exogenous inputs. Both cases of single-rate and multirate sampling are treated and general observer-based frameworks are provided using discrete-time approximation to estimate fault signals of any sources. We show that these frameworks are input-to-error stable with respect to the estimation error and can simultaneously enhance robustness against unknown inputs and sensitivity to faults in a mixed H−∕H∞ sense for the unknown exact discrete-time model of the plant. Our results are then applied to a class of Lipschitz nonlinear systems with a refined Euler approximate model to derive sampled-data fault estimation techniques where stability and H−∕H∞ optimization are ensured using linear matrix inequalities (LMIs). Simulation results of a flexible joint robot illustrate the effectiveness of the proposed methodologies.