Algorithms for worst case identification in <f>H∞</f> and in the <f>ν</f>-gap metric

This paper considers two robustly convergent algorithms for the identification of a linear system from (possibly) noisy frequency response data. Both algorithms are based on the same principle; obtaining a good worst case fit to the data under a smoothness constraint on the obtained model. However they differ in their notions of distance and smoothness. The first algorithm yields an FIR model of a stable system and is optimal, in a certain sense for a finite model order. The second algorithm may be used for modelling unstable plants and yields a real rational approximation in the <f>L2</f>-gap. Given a model and a controller stabilising the true plant, a procedure for winding number correction is also suggested. [Copyright &y& Elsevier]