ZKF-based optimal robust fault estimation of descriptor LPV systems with measurement error-affected scheduling variables.

This paper proposes a robust state and fault estimation (SFE) method for discrete-time descriptor linear-parameter-varying (LPV) systems with inexact scheduling variables. As an important robust method dealing with system uncertainties, the set-membership estimation method is combined with the technique of generalized fault detectability indices and matrix to compute a state and fault tube to contain the real system states and fault signals at each time instant under the assumption that the system uncertainties (i.e., modeling errors, process disturbances, measurement noises and errors of scheduling variables) are bounded to guarantee the robustness of SFE. Theoretically, any trajectory in the tube can be used as a point-wise estimation of the real system states and fault signals. Meanwhile, the optimal parametric matrices both for set-membership estimation and unknown input observer (UIO) are designed by using the zonotopic Kalman filter (ZKF) procedure to guarantee the optimality of SFE under a set-theoretic framework. Furthermore, a collection of stability conditions for the proposed optimal SFE method are established based on the linear matrix inequalities (LMIs). At the end, a practical electric circuit and a vehicle example are used to illustrate the effectiveness of the proposed SFE method.