This paper proposes a novel double switchings reliable control for positive switched systems. Double switchings refer to the switchings of subsystems and faults. Considering the actuator faults during the system operation, a class of periodic switched actuator faults is first considered. A reliable controller is designed using linear copositive Lyapunov functions and an average dwell time switching rule is presented for the systems. Then, two average dwell time switching rules are given for the subsystems and the faults, respectively. A corresponding reliable controller is proposed in terms of linear programming. Compared with existing results, the novel approach contains three advantages: (i) the actuator faults of subsystems are allowed to be varying, (ii) two classes of detailed double switchings rules are designed, and (iii) the presented reliable control framework provides a new methodology to deal with the reliable control problem of general switched systems with faults. Finally, two examples are given to illustrate the validity of the presented results.

中文翻译：

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双切换正切换系统的可靠执行器故障控制

本文提出了一种用于正切换系统的新型双切换可靠控制。双切换是指子系统和故障的切换。考虑系统运行过程中的执行器故障，首先考虑一类周期性开关执行器故障。使用线性共正李雅普诺夫函数设计了一个可靠的控制器，并给出了系统的平均驻留时间切换规则。然后，分别给出了子系统和故障的两个平均停留时间切换规则。根据线性规划提出了相应的可靠控制器。与现有结果相比，新方法包含三个优点：（i）子系统的执行器故障允许变化，（ii）设计了两类详细的双切换规则，(iii) 所提出的可靠控制框架提供了一种新的方法来处理具有故障的通用开关系统的可靠控制问题。最后，给出了两个例子来说明所呈现结果的有效性。