Robust fault detection observer design under fault sensitivity constraints

In this paper, a reduced-order robust fault detection observer (FDO) for continuous linear time-invariant systems with unknown inputs is designed by combining the algebraic unknown input decoupling principle with linear matrix inequalities (LMIs)-based optimization of fault sensitivity constraints. Algebraic unknown input decoupling is incorporated into the design of fault detection observers, thereby leading to a reduced-order robust FDO that is decoupled from unknown inputs. The gain matrix of the reduced-order robust FDO is determined from the optimal solution that maximizes the LMIs, which are based on the H_ index performance and the additional pole placement in a specified LMI region. This ensures that the designed robust FDO provides the optimal fault sensitivity on the residual. The efficiency of the proposed approach is evaluated through simulation studies and compared with the pole placement design and the mixed H_/H∞ observer given in the work of [9].