Robust State/Fault Estimation and Fault-Tolerant Control in Discrete-Time T-S Fuzzy Systems: An Embedded Smoothing...

This study investigates a simple design method of the robust state/fault estimation and fault-tolerant control (FTC) of discrete-time Takagi-Sugeno (T-S) fuzzy systems. To avoid the corruption of the fault signal on state estimation, a novel smoothing signal model of fault signal is embedded in the T-S fuzzy model for the robust H_∞ state/fault estimation of the discrete-time nonlinear system with external disturbance by the traditional fuzzy observer. When the component and sensor faults are generated from different fault sources, two smoothing signal models for component and sensor faults are both embedded in the T-S fuzzy system for robust state/fault estimation. Since the nonsingular smoothing signal model and T-S fuzzy model are augmented together for signal reconstruction, the traditional fuzzy Luenberger-type observer can be employed to robustly estimate state/fault signal simultaneously from the H_∞ estimation perspective. By utilizing the estimated state and fault signal, a traditional H_∞ observer-based controller is also introduced for the FTC with powerful disturbance attenuation capability of the effect caused by the smoothing model error and external disturbance. Moreover, the robust H_∞ observer-based FTC design is transformed into a linear matrix inequality (LMI) -constrained optimization problem by the proposed two-step design procedure. With the help of LMI TOOLBOX in MATLAB, we can easily design the fuzzy Luenberger-type observer for efficient robust H_∞ state/fault estimation and solve the H_∞ observer-based FTC design problem of discrete nonlinear systems. Two simulation examples are given to validate the performance of state/fault estimation and FTC of the proposed methods.