This work aims to study the problem of output strictly passive $$H_\infty $$ control for discrete-time linear switched singular systems. By using multiple storage functions and iteration technique, some sufficient conditions are obtained based on output strict passivity and proportional plus derivative state feedback, which can guarantee that the closed-loop systems are normal and stable and satisfy a given $$H_\infty $$ performance. Proportional plus derivative state feedback sub-controllers with explicit expressions are designed. Proportional plus derivative state feedback can not only eliminate impulse phenomena, but also eliminate state jumps caused by incompatible initial conditions of subsystems at switching instants. A numerical example is given to verify the applicability of the results.

中文翻译：

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输出严格无源 $${{\varvec{H}}_\infty }$$H∞ 通过比例加微分状态反馈控制离散时间线性切换奇异系统

这项工作旨在研究离散时间线性切换奇异系统的输出严格被动$$H_\infty $$控制问题。通过使用多重存储函数和迭代技术，基于输出严格无源性和比例加微分状态反馈得到一些充分条件，可以保证闭环系统正常稳定，满足给定的$$H_\infty $$表现。设计了具有显式表达式的比例加微分状态反馈子控制器。比例加微分状态反馈不仅可以消除脉冲现象，还可以消除子系统在切换瞬间初始条件不相容引起的状态跳跃。给出了一个数值例子来验证结果的适用性。