This paper presents a Fault Tolerant Control (FTC) scheme for systems with ${\mathcal{L}}_2$-bounded disturbances and generalized sector nonlinearity at the input. An adaptive observer-based fault estimation (FE) scheme is used to estimate the fault. The nonlinearity causes the control input (the measurable controller output, which is injected into the FE scheme) to differ from the actuator output (which enters the plant); this mismatch (together with the disturbances) causes interactions between the FE and FTC schemes, violating the separation principle and hence they cannot be designed separately. We introduce a method that integrates both FE and FTC schemes, and design them simultaneously (thus overcoming the violation of the separation principle), guaranteeing bounded stability. To obtain the sufficient conditions for stability and minimum ${\mathcal{L}}_2$-gain performance for disturbance rejection, we use the Sector Condition (SC) and successfully re-casted the design as Linear Matrix Inequalities (LMIs) which can be performed in a single step and yield tractable solutions. Through a numerical example, we demonstrate the effectiveness of the proposed method.

本文提出了具有以下特征的系统的容错控制（FTC）方案 ${\mathcal{大号}}_2$输入上的边界扰动和广义扇区非线性。自适应的基于观察者的故障估计（FE）方案用于估计故障。非线性导致控制输入（可测量的控制器输出，注入到FE方案中）与执行器输出（进入设备）不同；这种不匹配（以及干扰）会导致FE和FTC方案之间发生相互作用，从而违反了分离原理，因此无法单独设计它们。我们介绍了一种将FE和FTC方案集成在一起的方法，并同时设计它们（从而克服了分离原理的违反），从而保证了有限的稳定性。获得足够的稳定性和最小化条件${\mathcal{大号}}_2$为了获得抗干扰性能，我们使用了扇形条件（SC），并成功地将设计重铸为线性矩阵不等式（LMI），可以在一个步骤中完成并产生易于处理的解决方案。通过数值例子，我们证明了该方法的有效性。