A Comparison between Hankel Norms and Induced System Norms

©1998 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.A general definition is formulated for the Hankel norms as the induced norms of a strictly proper stable linear time-invariant (LTIV) system mapping vector-valued Lp-past inputs to vector-valued Lq-future outputs. Some Hankel norms are derived by the maximum principle and duality. A property termed the system integral invariance is introduced by the derivation of those Hankel norms. Furthermore, the norm-induced initial conditions and the comparison between the Hankel norms and the induced system norms are also presented