This paper deals with model-based fault detection and isolation problems, for linear time invariant systems subject to a large class of uncertainties and disturbances. A new approach based on non-smooth optimization techniques, is proposed to synthesize a state–space realization of the fault detection filter, within the $H_{\infty }/H_{-}$ setting. A set of new criteria for robust fault detection performance analysis is too proposed, using the generalized structured singular value theory. The proposed theories are illustrated on a satellite example, under a large class of nonlinear dependent uncertainties. Through a deep analysis of the example, it is shown how the $H_{\infty }/H_{-}$ design – ${\mu }_g$ analysis tools can serve as a general theory, to solve fault detection problems.

本文针对具有大量不确定性和干扰的线性时不变系统，处理基于模型的故障检测和隔离问题。提出了一种基于非平滑优化技术的新方法来综合故障检测滤波器的状态空间实现。$H_{\infty }/H_{-}$设置。还使用广义结构奇异值理论提出了一套用于鲁棒故障检测性能分析的新标准。在一大类非线性相关不确定性的情况下，在卫星示例上说明了所提出的理论。通过对示例的深入分析，可以看出$H_{\infty }/H_{-}$ 设计– ${\mu }_G$ 分析工具可以作为一般理论来解决故障检测问题。