An LMI approach to design robust fault detection observers

In this contribution, the robust fault detection observer design problem for LTI systems with both disturbances and modelling errors are studied. The basic idea of our study is to split the system state into plant state and the so called fault state, while the fault state is used to diagnose the occurrence of the fault. Then the main task of FDI becomes the fault state optimal estimation problem. Based on this, the FDI observer design problem is finally formulated as a two-objective H_∞-optimization and the LMI approach is developed. An illustrated numerical example is also presented to demonstrate the effectiveness of the proposed approach.