Model reduction is an important engineering problem in which one aims to replace an elaborate model by a simpler model without undue loss of accuracy. The accuracy can be mathematically measured in several possible rms and the Hankel rm is one such. The Hankel rm gives a meaningful tion of distance between two linear systems: roughly speaking, it is the induced rm of the operator that maps past inputs to future outputs. It turns out that the engineering problem of model reduction in the Hankel rm is closely related to the mathematical problem of finding solutions to the sub-optimal Nehari-Takagi problem, which is called the sub-optimal Hankel rm approximation problem in this book. Although the existence of a solution to the sub-optimal Hankel rm approximation problem has been kwn since the 1970's, this book presents explicit solutions and, in particular, new formulae for several large classes of infinite-dimensional systems for the first time.
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
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Lecture Notes in Control and Information Sciences
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Springer-Verlag Berlin and Heidelberg GmbH & Co. K