A QMI approach to the robust fault detection and isolation problem

Abstract

This chapter investigates the robust fault detection and isolation (FDI) problem for uncertain linear time-invariant (LTI) systems. An FDI filter minimizes the sensitivity of the residual signal to disturbances and modeling errors subject to the constraint that the transfer matrix function from the faults to the residual is closed to a diagonal transfer matrix function (for fault isolation). A solution of the optimization problem is presented via the formulation of a quadratic matrix inequality (QMI). The chapter gives a construction of a stable FDI filter that bounds the influence of the disturbances and model uncertainties on the residual signal measured in terms of the H∞-norm. The scheme implies that each element of the residual is only corresponding to a specified potential fault and therefore can handle multiple faults (where faults might occur at the same time). A jet engine example is employed to demonstrate the effectiveness of the obtained results.