中文摘要：

阐述了描述振动系统特性的几种范数。重点讨论了H2和H∞范数各自的特点及它们在振动控制中的物理含义及相关用途。分析了系统H∞范数的计算方法，并提出了一种优化算法。文中通过一个悬臂梁模型进行了仿真计算，验证了所提算法的正确性。研究表明，对于振动控制而言，从频带上来看，H2控制是同时抑制所有的共振峰，而H∞控制则仅抑制最大的共振峰。系统的H∞范数是诱导范数，它满足乘法特性，利用H∞范数可以方便地引入系统的非结构不确定性，进行振动控制系统的鲁棒性分析。

英文摘要：

Several norms to describe the properties of vibration systems are summarized. The H2 and H∞ norms and their applications in vibration control systems are discussed. The traditional calculation method for H∞ norm is recounted and a new optimization algorithm is built. A cantilever beam is used to verify the new algorithm. Finally conclusions are educed：in vibration control all the resonant peaks is pushed down with H2 norm control and only the largest resonant peak is attenuated with H∞ norm control. H∞ norm is a kind of induced norm and satisfies the multiplicative property. In robust control it is convenient to represent the unstructured model uncertainty by H∞ norm.