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The Covariance Extension Equation: A Riccati-type Approach to Analytic Interpolation

2020/10/14 by Yufang Cui, Anders Lindquist, Cui, Yufang +1
Engineering · Mathematics · Physics and Astronomy · #Control Systems and Identification #FOS: Mathematics #Model Reduction and Neural Networks #Numerical methods for differential equations #Optimization and Control (math.OC) #math.OC

paper · pdf · doi:10.48550/arxiv.2010.07081

openalex publication_date 2020/10/14 · openalex created_date 2020/10/22 · arxiv created 2021/07/25 · arxiv updated 2021/07/27 · openalex updated_date 2026/07/28

Abstract

Analytic interpolation problems with rationality and derivative constraints are ubiquitous in systems and control. This paper provides a new method for such problems, both in the scalar and matrix case, based on a non-standard Riccati-type equation. The rank of the solution matrix is the same as the degree of the interpolant, thus providing a natural approach to model reduction. A homotopy continuation method is presented and applied to some problems in modeling and robust control. We also address a question on the positive degree of a covariance sequence originally posed by Kalman.

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