Extended Balancing of Continuous LTI Systems: A Structure-Preserving Approach

• 成果类型: Article
• 署名作者: Borja, Pablo; Scherpen, Jacquelien M. A.; Fujimoto, Kenji
• 署名单位: Delft University of Technology; University of Groningen; Kyoto University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3138645
• 发表日期: 2023
• 页码: 257-271
• 关键词: Error bound; extended Gramians; Model reduction; port-Hamiltonian (PH) systems

摘要

In this article, we treat extended balancing for continuous-time linear time-invariant systems. We take a dissipativity perspective, thus, resulting in a characterization in terms of linear matrix inequalities. This perspective is useful for determining a priori error bounds. In addition, we address the problem of structure-preserving model reduction of the subclass of port-Hamiltonian systems. We establish sufficient conditions to ensure that the reduced-order model preserves a port-Hamiltonian structure. Moreover, we show that the use of extended Gramians can be exploited to get a small error bound and, possibly, to preserve a physical interpretation for the reduced-order model. We illustrate the results with a large-scale mechanical system example. Furthermore, we show how to interpret a reduced-order model of an electrical circuit again as a lower dimensional electrical circuit.