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

Yaoyao Tan, Xiaojie Su, Zhenshan Bing, Xiaokui Yang, Alois C. Knoll

Abstract: 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance level <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\xi, \beta)$</tex-math></inline-formula> . 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.