Norms

Abstract

System norms serve as a measure of system “size” and in this capacity they are used in the model reduction and in the actuator/sensor placement procedures. Three system norms: H₂, H_∞, and Hankel are analyzed in this book. It is shown that for flexible structures the H₂ norm has an additive property: it is a rootmean-square (rms) sum of the norms of individual modes. The H_∞ and Hankel norms are also determined from the corresponding modal norms, by choosing the largest one. All three norms of a structure with multiple inputs (or outputs) can be decomposed into the rms sum of norms of a structure with a single input (or output). These two properties allow for the development of unique and efficient model reduction methods and actuator/sensor placement procedures.