Fault detection based on zonotopic H_{_}/L_∞ observer for Lipschitz nonlinear systems

In this paper, for the Lipschitz nonlinear discrete system with unknown distributed and interference inputs characterized by bounded amplitudes, based on the reformulation of Lipschitz properties, the H_{_}/L_∞ fault observer is meticulously crafted to render the residual robust to disturbances and noise while maintaining sensitivity to faults. This design is transformed into a solution based on linear matrix inequalities. The feasible set of fault-free system residuals is obtained, and the fault detection is realized by comparing the residuals and feasible sets. Ultimately, the simulation is conducted using a single-link flexible robotic arm as an example to validate the effectiveness of the presented method.