Schur function minimization under Nevanlinna-Pick constraints : a convex approach
Résumé
In this paper we consider a Schur minimization problem in a frequency band under various constraints, which are relevant in engineering applications. These constraints include NP-interpolation conditions, a degree bound and the location of spectral zeros. We propose a relaxation of this initial problem, transforming it into a convex optimization problem. The relaxation concerns the degree constraint, but the degree remains bounded and the problem becomes tractable by nonlinear semi-definite programming techniques. The solution provides a bound on the minimal achievable norm for a Schur function satisfying the initial problem at a given degree. We illustrate our results with an application to the matching problem in filter design. We show that our method significantly improve on the Fano's bound, well-known in this context.
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
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