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.
Lu, Wayne W.; Balas, Gary J..
A Comparison between Hankel Norms and Induced System Norms.
Institute of Electrical and Electronic Engineers.
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