Schur function minimization under Nevanlinna-Pick constraints : a convex approach - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Schur function minimization under Nevanlinna-Pick constraints : a convex approach

Gibin Bose
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David Martínez Martínez
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Fabien Seyfert
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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.
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Dates et versions

hal-04675421 , version 1 (22-08-2024)

Identifiants

  • HAL Id : hal-04675421 , version 1

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Gibin Bose, David Martínez Martínez, Martine Olivi, Fabien Seyfert. Schur function minimization under Nevanlinna-Pick constraints : a convex approach. 2024. ⟨hal-04675421⟩
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