Abstract We address the state feedback stabilization of linear systems with input delay using the so-called act-and-wait control strategy. The latter approach induces an analysis of the closed-loop stability based on a finite-dimensional monodromy operator, and rendering this matrix nilpotent results in fixed-time stability. We show that any controllable planar system can be stabilized in a fixed time, and the constructive proof reveals that always two isolated solutions for the corresponding controller gain co-exist. Next, for the fixed-time stabilization of general linear systems, we present both a novel numerical approach for the computation of the controller gain, and an analytic approach relying on incorporating a predictor and an appropriately defined feedback transformation in the control scheme. Several illustrations complete the presentation.

中文翻译：

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基于动作等待控制的输入延迟系统的定时镇定

摘要 我们使用所谓的行为等待控制策略来解决具有输入延迟的线性系统的状态反馈稳定问题。后一种方法基于有限维单态算子对闭环稳定性进行分析，并使该矩阵幂零导致固定时间稳定性。我们表明，任何可控平面系统都可以在固定时间内稳定下来，并且建设性的证明表明，对于相应的控制器增益，总是有两个孤立的解决方案共存。接下来，对于一般线性系统的固定时间稳定，我们提出了一种用于计算控制器增益的新型数值方法，以及一种依赖于在控制方案中结合预测器和适当定义的反馈变换的分析方法。