Optimal thresholding for robust fault detection of uncertain systems

An important issue in fault diagnosis research is the design of methods for robust residual generation. In this framework, systems described by uncertain models and subject to unknown input disturbances are studied in this article. A nominal model of the system is first considered for residual generation using an H∞ parameterized output observer. The design procedure is based on the optimization of a performance index which is solved via linear matrix inequalities (LMI). Unstructured uncertainties due to parameter variations are then considered in the system model. In order to take the worst effect of uncertainties into account, the determination of an optimal threshold depending on the operating conditions is suggested for residual evaluation. This is achieved via the introduction of Kharitonov polynomials and the associated geometry of uncertain polytopic families. A simulation example illustrates the proposed approach.