IEEE Trans Cybern. 2015 Feb;45(2):229-41. doi: 10.1109/TCYB.2014.2323994. Epub 2014 Jun 5.
This paper focuses on the problem of fault detection for Takagi-Sugeno fuzzy systems with time-varying delays via delta operator approach. By designing a filter to generate a residual signal, the fault detection problem addressed in this paper can be converted into a filtering problem. The time-varying delay is approximated by the two-term approximation method. Fuzzy augmented fault detection system is constructed in δ -domain, and a threshold function is given. By applying the scaled small gain theorem and choosing a Lyapunov-Krasovskii functional in δ -domain, a sufficient condition of asymptotic stability with a prescribed H∞ disturbance attenuation level is derived for the proposed fault detection system. Then, a solvability condition for the designed fault detection filter is established, with which the desired filter can be obtained by solving a convex optimization problem. Finally, an example is given to demonstrate the feasibility and effectiveness of the proposed method.
本文针对时变时滞 Takagi-Sugeno 模糊系统的故障检测问题，采用微分算子方法进行研究。通过设计滤波器生成残差信号，将故障检测问题转化为滤波问题。采用两阶逼近法对时变时滞进行逼近。在 δ -域中构建模糊增广故障检测系统，并给出一个阈值函数。应用比例小增益定理，并在 δ -域中选择李雅普诺夫-克拉索夫斯基泛函，得到所提出的故障检测系统具有给定 H∞干扰衰减水平的渐近稳定性的充分条件。然后，建立了设计故障检测滤波器的可解性条件，通过求解凸优化问题得到期望滤波器。最后，通过一个实例验证了所提出方法的可行性和有效性。
