Abstract

First, an \({{H}_{\infty }}\) adaptive observer is designed for a class of uncertain nonlinear descriptor systems. This observer can simultaneously estimate the actuator faults, sensor faults, and system states in the presence of uncertainty and output disturbance. Various types of faults, such as abrupt faults and incipient faults, can be estimated using the observer. Then, the observer is designed without requiring some conditions to be satisfied. The observer stability is analyzed using the Lyapunov stability theory. Then, the sufficient conditions for the existence of the observer are converted into linear matrix inequalities (LMIs). The proposed method does not need the Lipschitz constant in the LMI formulation. Therefore, the proposed method can be applied to systems with unknown or large Lipschitz constants. Additionally, unlike the conventional adaptive estimator, the proposed estimator has both proportional and integral components to enhance the accuracy and rapidity of the estimation. Two simulation examples are provided to illustrate the effectiveness of the proposed method for descriptor systems and normal state-space systems.

中文翻译：

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一类不确定的非线性广义系统基于自适应观测器的故障估计

摘要

首先，一个\（{{H} _ {\ infty}} \）自适应观测器是为一类不确定的非线性描述系统设计的。在存在不确定性和输出干扰的情况下，该观察者可以同时估计执行器故障，传感器故障和系统状态。可以使用观察者来估计各种类型的故障，例如突然故障和初期故障。然后，设计观察者而无需满足一些条件。使用Lyapunov稳定性理论分析观察者的稳定性。然后，将观察者存在的充分条件转换为线性矩阵不等式（LMI）。所提出的方法在LMI公式中不需要Lipschitz常数。因此，所提出的方法可以应用于具有未知或大Lipschitz常数的系统。此外，与传统的自适应估算器不同，所提出的估计器具有比例和积分分量，以提高估计的准确性和快速性。提供了两个仿真示例，以说明所提出方法对描述符系统和正常状态空间系统的有效性。