A robust least square fault detection approach for linear systems with structured time-varying perturbations

This paper proposes a robust least square approach to the robust fault detection and estimation problem for a linear time-invariant (LTI) system. Rather than using a reference model and transfer the fault detection problem into a model-watching formulation, we provide a direct fault reconstruction approach to estimate the incoming fault signal. Unknown inputs, actuator faults, sensor faults and disturbances are considered in our design. A sufficient affine matrix inequality condition is developed which guarantees that the filter estimation error is kept below a specified level of performance index in the presence of disturbance and structured time-varying norm-bounded uncertainties. In order to transfer the nonlinear matrix inequality into a equivalent affine problem, we define certain congruence transformation parameters and provide an interior-point convex optimization method to obtain the convex solution. A numerical example is provided to confirm the effectiveness of our approach.