In this paper, an adaptive observer-based fault-tolerant control (FTC) strategy is proposed for a class of Takagi-Sugeno (T-S) fuzzy systems with both actuator and sensor faults under external disturbances. FTC approach is developed to compensate the actuator faults and to stabilize the faulty system. Furthermore, using H_∞ optimization technique, an adaptive fuzzy observer is developed, not only to achieve a simultaneous estimation of system states, sensor and actuator faults, but also to attenuate the influence of disturbances. In terms of linear matrices inequalities (LMIs), sufficient conditions of the existence of observer and controller are derived. We overcome the drawback of two-step algorithm by proposing a single-step one which allows to solve only the strict LMIs. Therefore, the obtained results present an acceptable compromise between conservatism reduction and computational complexity. Finally, two numerical examples which one of them is an application to a cart motion model are presented to demonstrate the usefulness of the proposed method.

本文针对一类在外部扰动下具有执行器和传感器故障的Takagi-Sugeno（TS）模糊系统，提出了一种基于观测器的自适应容错控制（FTC）策略。开发了FTC方法来补偿执行器故障并稳定故障系统。此外，使用ħ _∞通过优化技术，开发了一种自适应模糊观测器，不仅可以实现对系统状态，传感器和执行器故障的同时估计，而且可以减轻干扰的影响。根据线性矩阵不等式（LMI），得出了观察者和控制器存在的充分条件。通过提出仅允许解决严格的LMI的单步算法，我们克服了两步算法的缺点。因此，获得的结果在保守性降低和计算复杂性之间提出了可接受的折衷方案。最后，给出了两个数值示例，其中之一是应用于小车运动模型的，以证明该方法的有效性。