Fault detection observer design for interval type-2 T–S fuzzy systems based on locally optimized membership function-dependent H− performance

Abstract

A fault detection observer design method for interval Type-2 Takagi–Sugeno fuzzy systems based on a newly defined locally optimized membership function dependent $H_{-}$ performance index is proposed in this paper. In the field of fault detection, the $H_{-}$ performance index is a crucial measure of the sensitivity of residual signals to fault signals. Therefore, utilizing $H_{-}$ performance for fault detection observer design is common, and enhancing this index is significant for improving the sensitivity and reducing the false alarm rate of observers. This paper introduces a novel $H_{-}$ performance index, considering that Takagi–Sugeno fuzzy systems do not operate on all linear subsystems indefinitely. The focus is on enhancing the $H_{-}$ performance of subsystems operating for extended periods. Additionally, by partitioning the state space and fully utilizing upper and lower membership function information, the $H_{-}$ performance of locally dominant subsystems with high membership on long-running linear subsystems is improved. A novel locally optimized membership function-dependent $H_{-}$ performance index is thus defined. Moreover, combining the line-integral fuzzy Lyapunov function and descriptor system method, the relaxation variable technique is provided and overcomes the requirement for time derivatives of membership functions. The newly defined $H_{-}$ performance index introduces a novel approach to designing fault detection observers. By providing sufficient conditions for the existence of fault detection observers, this method offers promise for enhancing fault detection capabilities in systems. The simulation results further validate the effectiveness of this approach, indicating its potential for practical application.