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

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 i...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 69; no. 4; pp. 2629 - 2636
Main Authors: Chen, Yahao, Ghanes, Malek, Barbot, Jean-Pierre
Format: Journal Article
Language:English
Published: New York IEEE 01.04.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Subjects:
Algebra
Bicausal changes of coordinates
causality
Computer Science
Delays
Differential equations
Differential operators
differential-algebraic equations (DAEs)
Function approximation
implicit function theorem
Iterative algorithms
Iterative methods
Mathematics
Nonlinear systems
Optimization and Control
Systems and Control
Theorems
Time delay systems
time-delay
nonlinear systems
time-delay
bicausal changes of coordinates
differential-algebraic equations
implicit function theorem
causality
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary: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.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2023.3332205