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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Veröffentlicht in:	IEEE transactions on automatic control Jg. 69; H. 4; S. 2629 - 2636
Hauptverfasser:	Chen, Yahao, Ghanes, Malek, Barbot, Jean-Pierre
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.04.2024 The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Institute of Electrical and Electronics Engineers
Schlagworte:	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
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Abstract	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.
AbstractList	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. 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. 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 (DDAEs) to reduce their indices and to get their solutions. Some numerical examples are given to illustrate our results.
Author	Barbot, Jean-Pierre Ghanes, Malek Chen, Yahao
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References	ref13 ref12 ref30 ref11 ref10 ref2 Lee (ref26) 2001 ref1 ref17 ref16 ref19 ref18 Mrquez-Martnez (ref6) 2002; 38 Gantmacher (ref14) 1959 Campbell (ref15) 1991 ref24 ref23 ref25 ref20 ref22 ref21 ref28 ref27 ref29 ref8 ref7 ref9 ref4 ref3 ref5
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SubjectTerms	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
Title	Implicit Function Theorem for Nonlinear Time-Delay Systems With Algebraic Constraints
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