Robust, Positive, and Exact Model Reduction via Monotone Matrices

• 成果类型: Article
• 署名作者: Cortese, Marco; Grigoletto, Tommaso; Ticozzi, Francesco; Ferrante, Augusto
• 署名单位: University of Padua
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3569190
• 发表日期: 2025
• 页码: 6907-6912
• 关键词: VECTORS; reduced order systems; training; systematics; STANDARDS; Perturbation methods; Numerical models; Linear systems; indexes; Data mining; Model/controller reduction; positive systems

摘要

This work focuses on the problem of exact model reduction of positive linear systems, by leveraging minimal realization theory. While determining the existence of a positive reachable realization remains in general an open problem, we are able to fully characterize the cases in which the new model is obtained with nonnegative reduction matrices, and hence positivity of the reduced model is robust with respect to small perturbations of the original system. The characterization is obtained by specializing the monotone matrix theory to positive matrices. In addition, we provide a systematic method to construct positive reductions also when minimal ones are not available, by exploiting algebraic techniques.