An energetic approach is presented for the synthesis of polytopic fault observers for a class of discrete-time linear systems subject to multiplicative and additive faults. The main purpose of the proposed approach is to estimate the multiplicative component faults. The direct influence of fault occurrences on the system stability is considered in the design procedure. In the proposed approach, the unknown input-decoupling principle is used to decouple the component faults from sensor and actuator faults. Then, an algebraic technique is used to derive a regressor description of the system energy balance, where the regressor coefficients are component of the fault matrix elements. This formulation provides the possibility of using a Least-Squares technique to on-line component faults estimation. In order to estimate the component fault along with sensor faults, a new observer structure is proposed where the regressor description is coupled with the Unknown Input Observer by means of an auxiliary output.

提出了一种能量方法，用于合成一类受乘性和加性故障影响的离散时间线性系统的多面体故障观测器。所提出方法的主要目的是估计乘性组件故障。在设计过程中考虑了故障发生对系统稳定性的直接影响。在所提出的方法中，未知输入解耦原理用于将组件故障与传感器和执行器故障解耦。然后，使用代数技术推导出系统能量平衡的回归器描述，其中回归器系数是故障矩阵元素的组成部分。这个公式提供了使用最小二乘技术在线部件故障估计的可能性。