Fault detection and isolation filter design for systems subject to polytopic uncertainties

This paper considers the robust fault detection and isolation (FDI) problem for linear time-invariant dynamic systems subject to faults, disturbances and polytopic uncertainties. We employ an observer-based FDI filter to generate a residual signal. We propose a cost function that penalizes a weighted combination of the deviation of the fault to residual dynamics from a given fault isolation reference model, as well as the effects of disturbances and uncertainties on the residual, using the H-infinity norm as a measure. The proposed cost function thus captures the requirements of fault detection and isolation and disturbance rejection in the presence of polytopic uncertainties. We derive necessary and sufficient conditions for the existence of an FDI filter that achieves the design specifications. This condition takes the form of easily implementable linear matrix inequality (LMI) optimization problem.