Design of novel observers for robust fault detection in discrete-time lipschitz non-linear systems with euler-approximate models

This paper addresses the problem of observer-based robust fault detection in a class of Lipschitz non-linear systems. A Euler-approximate model for continuous-time Lipschitz non-linear systems is first established; then, a discrete time non-linear observer is designed such that the dynamic output-estimation error, which is assigned as a residual signal, asymptotically converges to zero if no actuator faults and external disturbances exist in the system. The new observer has similarity to a non-linear unknown input observer (UIO). Compared with the existing UIOs, the design of the presented observer requires fewer gain matrices and equation constraints; less computation load is therefore needed. On the other hand, the new observer is designed based on the Euler-approximate model. To ensure its implementation on the exact model, sufficient conditions for semiglobal practical convergence of the proposed observer are explicitly provided. With external disturbances, a nonlinear H _∞ observer is constructed to achieve robust actuator fault detection. Observer design problem can be systematically solved using linear matrix inequality (LMI)-based optimisation technique. Lastly, a single-link flexible robot is employed to illustrate the effectiveness of the proposed observer-based FD scheme.