SummaryThis paper addresses the problem of switching control for systems subject to external disturbances that vary over multiple frequency ranges. Specifically, two different scenarios of disturbance injection are considered; namely, the disturbance may switch between different prescribed frequency ranges, subject to an average dwell time setting, or the disturbance may reside within one of the frequency ranges. To address these scenarios, a disturbance‐triggered control scheme is developed that divides the entire frequency range into low‐, mid‐, and high‐frequency ranges. This scheme ensures closed‐loop stability under average dwell time frequency‐range switching and achieves performance when operated under individual frequency ranges. Synthesis conditions in matrix inequalities are derived to characterize the switching control, and an iterative algorithm is proposed for finding a desired set of controller gains. Finally, two examples are presented to illustrate the effectiveness of the proposed control method.

中文翻译：

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H∞ 多个频率范围内扰动切换的衰减

摘要本文解决了受多个频率范围内变化的外部干扰影响的系统的切换控制问题。具体来说，考虑了两种不同的扰动注入场景；即，扰动可以在不同的规定频率范围之间切换，服从平均停留时间设置，或者扰动可以驻留在频率范围之一内。为了解决这些情况，开发了一种干扰触发控制方案，将整个频率范围分为低频、中频和高频范围。该方案确保了平均驻留时间频率范围切换下的闭环稳定性，并在各个频率范围下运行时实现了性能。导出了矩阵不等式中的综合条件来表征开关控制，并提出了一种迭代算法来找到一组所需的控制器增益。最后，给出两个例子来说明所提出的控制方法的有效性。