This work focuses on the problem of fault-tolerant control for nonlinear persistent dwell-time (PDT) switched singularly perturbed systems (SPSs) with time-varying delays. The persistent dwell-time switching mechanism is employed to describe the fast and slow switching among several subsystems in the investigated systems alternatively. In order to reduce the influence of actuator faults on system stability and performance, a fault-tolerant feedback controller is designed. Based on Lyapunov function approach and Takagi–Sugeno fuzzy technique, some sufficient conditions are obtained, which can ensure the exponentially stable and \({H_\infty }\) performance of the closed-loop system. In addition, the fault-tolerant slow state variables feedback (SSVF) controller is obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example, an inverted pendulum model, and a tunnel diode circuit model are given to show the practicability and usefulness of the developed control scheme.

这项工作侧重于具有时变延迟的非线性持久驻留时间 (PDT) 切换奇异扰动系统 (SPS) 的容错控制问题。采用持久驻留时间切换机制来交替描述所研究系统中几个子系统之间的快速和慢速切换。为了减少执行器故障对系统稳定性和性能的影响，设计了一种容错反馈控制器。基于Lyapunov函数方法和Takagi-Sugeno模糊技术，得到了一些充分条件，可以保证指数稳定和\({H_\infty }\)闭环系统的性能。此外，容错慢状态变量反馈（SSVF）控制器是通过求解一组线性矩阵不等式（LMI）获得的。最后，给出了一个数值例子、一个倒立摆模型和一个隧道二极管电路模型，以表明所开发的控制方案的实用性和有用性。