Hankel norm approximation for infinite-dimensional systems

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 norms and the Hankel norm is one such. The Hankel norm gives a meaningful notion of distance between two linear systems: it is the induced norm of the operator that maps past inputs to future outputs. It turns out that the engineering problem of model reduction in the Hankel norm is closely related to the mathematical problem of finding solutions to the sub-optimal Nehari-Takagi problem, which we prefer to call "the sub-optimal Hankel norm approximation problem" in this thesis. Although the solution to the sub-optimal Hankel norm approximation problem has been known since the 1970's, in this thesis, we give an alternative derivation and, in particular, we give new explicit formulae for some special classes. ... Zie: Summary