The ‐gain analysis and fault‐tolerant control of a class of uncertain nonlinear discrete‐time switched systems with time‐varying delay and actuator saturation are studied by using the multiple Lyapunov functions method. The fault‐tolerant state feedback controllers and the switching law are designed such that the closed‐loop system with actuator failures satisfies the disturbance attenuation performance indicator. The problem of estimating the capacity of admissible disturbance is transformed into a constrained optimization problem to ensure that the state trajectory of the closed‐loop system is bounded under the action of external disturbances. The upper bound of restricted ‐gain is estimated by solving constrained optimization problems. Then, when the fault‐tolerant controller can be regard as the design variable, the optimization problems above are adjusted for solving control synthesis problems. Finally, the numerical example is given to verify the effectiveness of the design method.

中文翻译：

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L2$$ {L}_2 $$-具有时变延迟和执行器饱和的非线性离散时间切换系统的增益分析和容错控制

利用多重Lyapunov函数方法研究了一类具有时变时滞和执行器饱和的不确定非线性离散时间切换系统的增益分析和容错控制。设计容错状态反馈控制器和切换律，使得执行器故障的闭环系统满足扰动衰减性能指标。将估计容许扰动能力的问题转化为约束优化问题，以保证闭环系统在外部扰动作用下的状态轨迹有界。受限增益的上限是通过解决约束优化问题来估计的。然后，当容错控制器可以作为设计变量时，对上述优化问题进行调整以解决控制综合问题。最后给出数值算例验证了设计方法的有效性。