Reduced Model-Based Fault Detector and Controller Design for Discrete-Time Switching Fuzzy Systems

The reduced model-based coordinated design of fault detectors and controllers for discrete-time switching fuzzy systems is examined. First, the mean-square exponential stabilization of switching Takagi-Sugeno fuzzy systems is performed using the average dwell time method under an arbitrary switching law. Next, using segmented Lyapunov function techniques, a dynamic full- and reduced-order fault detector and controller is designed to ensure that the overall dynamic residual system is mean-square exponentially stable with a balanced $\mathcal {H}_{\infty }$ performance level $(\xi, \beta)$. The solvability conditions for the fault detector and controller are derived using a linearization method, and the relevant parameters can be determined using the mathematical linear matrix solver toolbox. Two examples including a switching Chua's circuit system are presented to demonstrate the effectiveness of the proposed fault detector and controller.