Balanced Truncation of k-Positive Systems

• 成果类型: Article
• 署名作者: Grussler, Christian; Damm, Tobias; Sepulchre, Rodolphe
• 署名单位: University of California System; University of California Berkeley; University of Kaiserslautern; Fraunhofer Gesellschaft; Fraunhofer Germany; Fraunhofer Industrial Mathematics; University of Cambridge
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3075319
• 发表日期: 2022
• 页码: 526-531
• 关键词: External positivity; internal positivity; k-positivity; model order reduction; nonnegative matrix factorization; positive systems; total positivity

摘要

This article considers balanced truncation of discrete-time Hankel k-positive systems, characterized by Hankel matrices whose minors up to order k are nonnegative. Our main result shows that if the truncated system has order k or less, then it is Hankel totally positive (8-positive), meaning that it is a sum of first-order lags. This result can be understood as a bridge between two known results: the property that the first-order truncation of a positive system is positive (k = 1), and the property that balanced truncation preserves state-space symmetry. It provides a broad class of systems where balanced truncation is guaranteed to result in a minimal internally positive system.