Fault Detection for T–S Fuzzy Systems With Unknown Membership Functions

Abstract

This paper is concerned with the fault detection (FD) problem for Takagi-Sugeno (T-S) fuzzy systems with unknown membership functions. If the membership functions are unknown, the linear FD filter designs with fixed gains have been considered in the literature. To reduce the conservatism of the existing results, a switching mechanism that depends on the lower and upper bounds of the unknown membership functions is provided to construct an FD filter with varying gains. It is shown that the switching-type FD filter with varying gains can achieve a better FD performance than the linear FD filter with fixed gains. In addition, based on some time-domain inequalities, a novel weighting matrix design approach is introduced to transform the fault sensitivity specification into an H ∞ constraint. Finally, two examples are given to show the advantages of the proposed FD method. Index Terms-Fault detection (FD), switching-type filter, Takagi-Sugeno (T-S) fuzzy systems, unknown membership functions.

Fault detection for singular multiple time-delay systems with application to electrical circuit

“…Moreover, via the Lyapunov function approaches given in [12,19,20], one can obtain the corresponding FD filter design conditions. It should be pointed out that, by using the method of [2], the weighting matrices in Eq. (70) are selected as To see the advantages of our method more clearly, some comparison simulation results are also given.…”

“…Among these approaches, the celebrated H À =H 1 FD scheme is accepted as a popular and useful one. For instance, a weighting matrix is introduced in [1,2] to transform the fault sensitivity performance into an H 1 constraint; in [3][4][5], the H 1 and H À indexes are used to directly measure the fault sensitivity performance and the disturbance attenuation performance, respectively.…”

Adaptive fault estimation for T-S fuzzy systems with unmeasurable premise variables

“…For example, in [3], the problem of fault detection for nonlinear discrete-time networked systems under an event-triggered scheme was investigated, in [4], H 2 fault-detection observer for two-dimensional (2-D) discrete-time Markovian jump systems was proposed, and in [5], a simultaneous fault-detection and control strategy was proposed for switched linear systems with mode-dependent average dwell-time. In [6,7], fuzzy fault-detection observers were designed, particularly, a switching mechanism that depends on the lower and upper bounds of the unknown membership functions is provided to reduce conservatism in [6], and an integrated observer-based fault-detection scheme was proposed to meet the real-time fault-detection requirements from industrial processes in [7]. In [8], a fault-detection and -isolation (FDI) scheme for a class of Lipschitz nonlinear systems with nonlinear and unstructured modeling uncertainty was presented, and in [9], actuator stuck faults, including outage cases, were de-tected for linear state-feedback systems.…”

“…For discrete-time T-S fuzzy system influenced by sensor faults and unknown disturbances, an H -/H ∞ robust fault-detection observer was proposed in [20] by using descriptor approach and nonquadratic Lyapunov functions, whereas the T-S fuzzy systems with unmeasurable premise variables were considered in [21]. A fault-detection filter with varying gains was designed in [6] via a switching mechanism that depends on the membership function information. In addition, adaptive fuzzy observers have been used to estimate disturbances, faults or unmodeled dynamics of practical systems, such that practical nonlinear systems can be better approximated by T-S fuzzy systems.…”

Fault Detection for Discrete Systems With Network-Induced Nonlinearities

“…To improve the robustness of the system, it is crucial to detect and identify the faults and failures, when they occur as quickly as possible to make further decisions and remedies. In recent years, intensive attention has been paid on fault detection of various dynamic systems, and numerous significant results have been published in the literatures [3], [4], [7]- [9], [12]- [14], [20], [21], [25]- [27].…”