Steady-State Cascade Operators and Their Role in Linear Control, Estimation, and Model Reduction Problems

• 成果类型: Article
• 署名作者: Simpson-Porco, John W.; Astolfi, Daniele; Scarciotti, Giordano
• 署名单位: University of Toronto; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Engineering & Systems Sciences (INSIS); Universite Lyon 1; Imperial College London
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3587949
• 发表日期: 2026
• 关键词: NONLINEAR-SYSTEMS; output regulation; SYLVESTER; observability; stabilization; feedforward

摘要

Certain linear matrix operators arise naturally in systems analysis and design problems involving cascade interconnections of linear time-invariant systems, including problems of stabilization, estimation, and model order reduction. We conduct here a comprehensive study of these operators and their relevant system-theoretic properties. The general theory is leveraged to delineate both known and new design methodologies for control and observation of cascades, and to characterize structural properties of reduced models. Several entirely new designs arise from this systematic categorization, including new recursive and low-gain design frameworks for observation of cascaded systems. The benefits of the results beyond the linear time-invariant setting are demonstrated through preliminary extensions for nonlinear systems, with an outlook toward the development of a similarly comprehensive nonlinear theory.