非周期采样下系统稳定性条件的改进：基于模型和数据的分析
Improved stability conditions for systems under aperiodic sampling: model- and data-based analysis
摘要：
非周期采样下的离散时间系统可以作为信息物理和网络控制系统中出现的大量问题的建模抽象。最近，基于模型和数据的稳定性条件，这样的系统得到重写它们作为一个线性时不变系统和延迟算子的互连，随后，执行一个强大的稳定性分析，使用已知的约束上的增益，这个操作。在本文中，我们改进这种方法：首先，我们表明，延迟算子是输入前馈被动的，第二，我们准确地计算其增益。基于这些研究结果，我们得到改进的稳定性条件的情况下，充分的模型知识，只有数据可用。在后者中，我们只需要一个有限长度和潜在的噪声状态输入轨迹的未知系统。在两个例子中，我们说明了现有的建议的稳定性条件的保守性降低。
英文摘要：
Discrete-time systems under aperiodic sampling may serve as a modeling abstraction for a multitude of problems arising in cyber-physical and networked control systems. Recently, model- and data-based stability conditions for such systems were obtained by rewriting them as an interconnection of a linear time-invariant system and a delay operator, and subsequently, performing a robust stability analysis using a known bound on the gain of this operator. In this paper, we refine this approach: First, we show that the delay operator is input-feedforward passive and second, we compute its gain exactly. Based on these findings, we derive improved stability conditions both in case of full model knowledge and in case only data are available. In the latter, we require only a finite-length and potentially noisy state-input trajectory of the unknown system. In two examples, we illustrate the reduced conservativeness of the proposed stability conditions over existing ones.
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