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

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 H∞ performance level (ξ, β). 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.

Dissipative fault detection for time‐delay nonlinear Markov jump systems with measurement outliers under stochastic communication protocol

“…For example, a typical nonlinear system called Lur'e system, such as Chua's circuit and Lorenz system, can be seen as a system consisting of a linear term and a nonlinear term with sector‐bounded constraint 47 . The specific example of sector‐bounded nonlinearity can be seen the Chua's circuit studied in References 48 and 49. In this article, the problem of outlier‐resistant FD filter design for MJSs with sector‐bounded nonlinearity has been studied, which has certain theoretical significance and application space.…”

“…$$$ \hat{\beta}{V}_{A,1}\left(t-{\tau}_t\right) $$$ describes the delayed voltage feedback signal with $$$ {\tau}_t $$$ denoting the bounded time‐varying delay. Referring to Reference 49, the parameters in Chua's circuit () are set as $$$ {C}_{A,1}=0.764 $$$, $$$ {C}_{A,2}=8 $$$, $$$ {R}_{A,1}=1.637 $$$, $$$ {R}_{A,2}=2 $$$, $$$ {R}_B=0.012 $$$, $$$ {L}_A=0.8 $$$, $$$ {G}_a=-0.3 $$$, $$$ {G}_b=-0.01 $$$, $$$ \overline{V}=1 $$$ and $$$ \hat{\beta}=0.1 $$$. Let the state vector to be …”