关于弦稳定性的一个全面的不可能结果
Towards a comprehensive impossibility result for string stability
摘要：
我们提供了一个全面的不可能实现字符串的稳定性，即保持本地相对误差检查与本地控制器独立的子系统链的大小。我们显着扩展现有的结果，从LTI设置到任何齐次控制器，可以是非线性的，时变的，和本地通信。我们证明了这种不可能性的一组定义与各种规范的选择，包括$L_2$型，这是更标准的文献和BIBO型标准。所有结果都适用于一般的离散时间控制器，它应该涵盖大多数应用。
英文摘要：
We provide a comprehensive impossibility result towards achieving string stability, i.e. keeping local relative errors in check with local controllers independently of the size of a chain of subsystems. We significantly extend existing results, from the LTI setting to any homogeneous controllers that can be nonlinear, time-varying, and locally communicating. We prove this impossibility for a set of definitions with various norm choices, including the $L_2$-type which is more standard in the literature and a BIBO type criterion. All results hold for a general discrete-time controller which should cover most applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
