Displacement structure and \({\mathcal H}_\infty\) problems (Q2724379)

The Schur algorithm associates to a function analytic and contractive in the open unit disk a sequence of numbers of modulus less than \(1\) (the last one being of modulus \(1\) if the sequence is finite) This sequence of numbers plays a central role in various domains such as interpolation of bounded analytic functions and system theory (in particular prediction theory). The Schur algorithm has been extended to more general settings. A number of approaches are possible. The one considered here is based on the notion of displacement structure. The authors in particular review how, in this approach, the Schur algorithm is extended to the so-called non stationary (or timefvarying case), where bounded analytic functions are replaced by bounded upper triangular operators. The authors also list a number of issues that deserve further studies, such as relationships with state space methods.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00036].