This paper characterises and analyses the minimum detectable fault (MDF) (named generalised MDF here) for multiple multiplicative actuator faults based on set-separation constraints of healthy and faulty residual sets for discrete-time linear parameter varying (LPV) systems with bounded inputs and uncertainties. First, multiple multiplicative actuator faults are equivalently transformed into the form of multiple additive actuator faults for the sake of obtaining the simplified faulty residual set explicitly. Then, two different generalised MDF for different multiple actuator faults are, respectively, defined, which can be computed via solving simple linear programming (LP) problems. Moreover, we propose three detectability conditions to guarantee the detection of multiple multiplicative actuator faults by using the invariant set-based method. Finally, we provide effective selection guidance for the detection of different multiple multiplicative actuator faults by systematically analysing the conservatism and characteristics of these three guaranteed detectability conditions. At the end of this paper, an electrical circuit example is used to illustrate the effectiveness of the proposed method.

中文翻译：

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使用不变量集对离散时间 LPV 系统进行多执行器故障可检测性分析

本文基于具有有界输入的离散时间线性参数变化 (LPV) 系统的健康和故障残差集的集分离约束，表征和分析了多个乘法执行器故障的最小可检测故障 (MDF)（此处称为广义 MDF）。不确定性。首先，为了明确地获得简化的故障残差集，将多个乘性执行器故障等价转换为多个加性执行器故障的形式。然后，分别定义了针对不同的多个执行器故障的两种不同的广义 MDF，可以通过解决简单的线性规划 (LP) 问题来计算。此外，我们提出了三个可检测性条件，以保证使用基于不变集的方法检测多个乘法执行器故障。最后，我们通过系统地分析这三个保证可检测性条件的保守性和特征，为检测不同的多重乘法执行器故障提供有效的选择指导。在本文的最后，一个电路例子被用来说明所提出方法的有效性。