Implicit Function Theorem for Nonlinear Time-Delay Systems With Algebraic Constraints

• 成果类型: Article
• 署名作者: Chen, Yahao; Ghanes, Malek; Barbot, Jean-Pierre
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); Nantes Universite; Ecole Centrale de Nantes
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3332205
• 发表日期: 2024
• 页码: 2629-2636
• 关键词: Bicausal changes of coordinates; causality; Differential-algebraic equations (DAEs); Implicit function theorem; Nonlinear systems; time-delay

摘要

In this note, we discuss a generalization of the well-known implicit function theorem to the time-delay case. We show that the latter problem is closely related to the bicausal changes of coordinates of time-delay systems [Califano and Moog (2014), Califano and Moog (2017)]. An iterative algorithm is proposed to check the conditions and to construct the desired bicausal change of coordinates for the proposed implicit function theorem. Moreover, we show that our results can be applied to delayed differential-algebraic equations to reduce their indices and to get their solutions. Some numerical examples are given to illustrate our results.