## Norms

^ how to quantify structuraidynamics

Measure what is measurable, and make measurable what is not so.

â€”Galileo Galilei

System norms serve as a measure of intensity of its response to standard excitations, such as unit impulse, or white noise of unit standard deviation. The standardized response allows comparing different systems. Three system norms, H2, Hm, and Hankel are used in this book. We show that for flexible structures the H2 norm has an additive property: it is a root-mean-square (rms) sum of the norms of individual modes. We also show that the Hm and Hankel norms are determined from the corresponding modal norms, by selecting the largest one. All three norms of a mode with multiple inputs (or outputs) can be decomposed into the rms sum of norms of a mode with a single input (or output). Later in this book these two properties allow for the development of unique and efficient model reduction methods and actuator/sensor placement procedures.

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