The paper proposes several fault-tolerant control (FTC) laws for singularly perturbed systems (SPS) with actuator faults and disturbances. On of the main challenges in this context is that the fast-slow decomposition is not available for actuator faults and disturbances. In view of this, some conditions for the asymptotic stability of the closed-loop dynamics are investigated by amending the composite Lyapunov approach. On top of this, a closed-form expression of the upper-bound of singular perturbation parameter (SPP) is provided. Moreover, we design several SPP-independent composite FTC laws which can be applied when this parameter is unknown. Finally, the chattering phenomenon is eliminated by using the continuous approximation technique. We also emphasize that, for linear SPSs, the FTC design can be formulated as a set of linear matrix inequalities while the SPP upper-bound can be obtained by solving a convex optimization problem. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.

中文翻译：

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具有执行器故障和扰动的奇异摄动系统的容错控制

本文针对具有执行器故障和扰动的奇异扰动系统 (SPS) 提出了几种容错控制 (FTC) 定律。在这方面的主要挑战之一是快慢分解不适用于执行器故障和干扰。鉴于此，通过修正复合Lyapunov方法，研究了闭环动力学渐近稳定性的一些条件。在此之上，提供了奇异扰动参数 (SPP) 上界的闭式表达式。此外，我们设计了几个独立于 SPP 的复合 FTC 定律，当该参数未知时可以应用这些定律。最后，通过使用连续逼近技术消除了抖动现象。我们还强调，对于线性 SPS，FTC 设计可以表述为一组线性矩阵不等式，而 SPP 上限可以通过求解凸优化问题获得。给出了两个数值例子来说明所提出方法的有效性。