网络化控制系统基于样本的谱半径估计及稳定性检验
Finite-sample-based Spectral Radius Estimation and Stabilizability Test for Networked Control Systems
摘要：
在离散线性定常系统的分析与控制中，系统状态矩阵的谱半径起着至关重要的作用。通常，假设系统矩阵是已知的，从该矩阵可以直接计算谱半径。相反，我们考虑系统受过程噪声影响的设置，并且系统输入和状态测量的样本只有1000个。我们提供了两种方法来估计的谱半径，并推导出误差界，持有高概率。此外，我们展示了如何使用推导出的结果来测试稳定性的网络控制系统（NCSs）与有损通道时，只有1000多个样本的系统输入，状态和丢包序列。
英文摘要：
In the analysis and control of discrete-time linear time-invariant systems, the spectral radius of the system state matrix plays an essential role. Usually, it is assumed that system matrices are known, from which the spectral radius can be directly computed. Instead, we consider the setting where the system is affected by process noise, and one has only finitely many samples of system input and state measurements. We provide two methods for estimating the spectral radius and derive error bounds that hold with high probability. Moreover, we show how to use the derived results to test stabilizability for networked control systems (NCSs) with lossy channels when only finitely many samples of the system input, state, and packet drop sequence are available.
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