This article studies the H_∞ fault estimation (FE) problem for linear discrete time‐variant systems with actuator and sensor saturations. To handle the saturation nonlinearities for FE problem, a pair of an auxiliary linear model and an associated performance function augmenting from the conventional H_∞ performance index are constructed. Based on this pair, the original FE problem is readdressed as a two‐step optimization issue with an indefinite quadratic cost function. For a feasible optimization solution, the partial equivalence between a stationary point for a quadratic optimization problem and a projection for vectors in indefinite inner‐product space is utilized. A Krein‐space based inner product interpretation for the indefinite cost function is established and optimal linear estimation technique is employed to derive the stationary point of the aforementioned indefinite quadratic cost function. The existence condition of the fault estimator is explicitly obtained, and the fault is reconstructed analytically via a forward recursion algorithm. Two examples are given to show the effectiveness of the proposed FE scheme.

中文翻译：

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受执行器和传感器饱和影响的离散时变系统的故障估计

本文研究ħ _∞故障估计（FE）的问题与致动器和传感器的饱和度线性离散时变系统。为了处理为FE问题，一对辅助线性模型，并从常规的相关联的性能函数增广的饱和非线性ħ _∞构建性能指标。基于这一对，原始的有限元问题被重新解决为具有不确定二次成本函数的两步优化问题。对于可行的优化解决方案，利用了二次优化问题的固定点与不确定内积空间中向量的投影之间的局部等价关系。建立了基于Krein空间的不定成本函数的内积解释，并采用最佳线性估计技术来推导上述不定二次成本函数的平稳点。明确获得了故障估计器的存在条件，并通过前向递归算法对故障进行了解析重建。给出两个例子来说明所提出的有限元方案的有效性。