论文标题
输入输出伪谱界限用于网络和高级系统的瞬态分析
Input-Output Pseudospectral Bounds for Transient Analysis of Networked and High-Order Systems
论文作者
论文摘要
我们需要以相关的信号规范和最坏情况输入方案来表征大型网络系统中的瞬态行为的动机，我们提出了一种基于矩阵pseudospectra的现有理论的新方法。我们将与矩阵指数有关的伪谱定理扩展到输入输出设置，其中矩阵指数由输入和输出矩阵预先进行了矩阵指数。分析复杂平面中所得的传输函数使我们能够在系统瞬变上陈述新的上限和下限。这些对于高阶矩阵微分方程很有用，特别控制了双整合器网络，例如车辆形成问题。因此，我们说明了该理论对车辆排的问题和弦稳定性问题的适用性，并展示了如何直接从输入输出伪斑点直接识别和量化不利的瞬态行为。
Motivated by a need to characterize transient behaviors in large network systems in terms of relevant signal norms and worst-case input scenarios, we propose a novel approach based on existing theory for matrix pseudospectra. We extend pseudospectral theorems, pertaining to matrix exponentials, to an input-output setting, where matrix exponentials are pre- and post-multiplied by input and output matrices. Analyzing the resulting transfer functions in the complex plane allows us to state new upper and lower bounds on system transients. These are useful for higher-order matrix differential equations, and specifically control of double-integrator networks such as vehicle formation problems. Therefore, we illustrate the theory's applicability to the problem of vehicle platooning and the question of string stability, and show how unfavorable transient behaviors can be discerned and quantified directly from the input-output pseudospectra.
