Fault estimation for discrete time-variant systems subject to actuator and sensor saturations

This article studies the H_∞ fault estimation (FE) problem for linear discrete time-variant systems with actuator and sensor saturations. To handle the saturation nonlinearities for FE problem, a pair of an auxiliary linear model and an associated performance function augmenting from the conventional H_∞ performance index are constructed. Based on this pair, the original FE problem is readdressed as a two-step optimization issue with an indefinite quadratic cost function. For a feasible optimization solution, the partial equivalence between a stationary point for a quadratic optimization problem and a projection for vectors in indefinite inner-product space is utilized. A Krein-space based inner product interpretation for the indefinite cost function is established and optimal linear estimation technique is employed to derive the stationary point of the aforementioned indefinite quadratic cost function. The existence condition of the fault estimator is explicitly obtained, and the fault is reconstructed analytically via a forward recursion algorithm. Two examples are given to show the effectiveness of the proposed FE scheme.