结构化线性定常系统的最优性条件

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-04-22 DOI:10.1137/23m1610033

Petar Mlinarić, Peter Benner, Serkan Gugercin

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引用次数: 0

摘要

SIAM数值分析杂志，第63卷，第2期，第949-975页，2025年4月。摘要。非结构化线性时不变系统的数学最优降阶建模的插值必要最优性条件是众所周知的。基于先前关于平稳参数问题的[math]-最优降阶建模的工作，在本文中，我们开发并研究了结构化LTI系统的[math]-最优降阶建模的最优性条件，特别是二阶，port- hamilton和时滞系统。在一定的对角化假设下，我们证明了在所有这些不同的结构设置中，双向Hermite插值是最优性的常见形式，从而证明了结构化降阶建模的统一最优性框架。

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Interpolatory [math]-Optimality Conditions for Structured Linear Time-Invariant Systems

SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 949-975, April 2025.
Abstract. Interpolatory necessary optimality conditions for [math]-optimal reduced-order modeling of unstructured linear time-invariant (LTI) systems are well-known. Based on previous work on [math]-optimal reduced-order modeling of stationary parametric problems, in this paper, we develop and investigate optimality conditions for [math]-optimal reduced-order modeling of structured LTI systems, in particular, for second-order, port-Hamiltonian, and time-delay systems. Under certain diagonalizability assumptions, we show that across all these different structured settings, bitangential Hermite interpolation is the common form for optimality, thus proving a unifying optimality framework for structured reduced-order modeling.

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.