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

被引：0

作者：

Chen, Yahao ^{[1
]}

Ghanes, Malek ^{[1
]}

Barbot, Jean-Pierre ^{[1
,2
]}

机构：

[1] Nantes Univ, CNRS, Cent Nantes, UMR 6004,LS2N, F-44300 Nantes, France

[2] ENSEA, Quartz EA 7393, F-95000 Cergy, France

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2024年 / 69卷 / 04期

关键词：

Bicausal changes of coordinates; causality; differential-algebraic equations (DAEs); implicit function theorem; nonlinear systems; time-delay; NUMERICAL-SOLUTION; EQUATIONS; OBSERVABILITY; STABILITY;

D O I：

10.1109/TAC.2023.3332205

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

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.

引用

页码：2629 / 2636

页数：8

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