Minimal Realizations of Nonlinear Time-Delay Systems

• 成果类型: Article
• 署名作者: Kaldmae, Arvo; Bartosiewicz, Zbigniew; Kotta, Ulle; Wyrwas, Malgorzata
• 署名单位: Bialystok University of Technology; Tallinn University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3240124
• 发表日期: 2023
• 页码: 6766-6772
• 关键词: Algebraic methods; minimal state-space realization; Nonlinear systems; time-delay systems.

摘要

The problem of finding a minimal realization of a single-input-single-output nonlinear retarded time-delay input-output equation with constant commensurable delays is addressed. First, an algorithm is given to find an observable realization of dimension n of a nth order input-output equation. Then, this algorithm is modified under two technical assumptions to find a realization of lower dimension, which is observable and accessible. It is shown that under the same technical assumptions an observable and accessible realization has minimal possible state-space dimension among all possible realizations. An algebraic approach based on polynomial tools and modules of differential 1-forms is used to derive the results.