A subspace-based method for solving Lagrange-Sylvester interpolation problems

Akcay H., Turekay S.

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, vol.29, no.2, pp.377-395, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 2
  • Publication Date: 2007
  • Doi Number: 10.1137/050622171
  • Journal Name: SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.377-395
  • Keywords: rational interpolation, Lagrange-Sylvester, identification, subspace-based, FREQUENCY-RESPONSE DATA, RATIONAL INTERPOLATION, SYSTEM-IDENTIFICATION, OPTIMIZATION
  • Anadolu University Affiliated: No

Abstract

In this paper, we study the Lagrange-Sylvester interpolation of rational matrix functions which are analytic at infinity, and propose a new interpolation algorithm based on the recent subspace-based identification methods. The proposed algorithm is numerically efficient and delivers a minimal interpolant in state-space form. The solvability condition for the subspace-based algorithm is particularly simple and depends only on the total multiplicity of the interpolation nodes. As an application, we consider subspace-based system identification with interpolation constraints, which arises, for example, in the identification of continuous-time systems with a given relative degree.