Implicit function theorem for nonlinear time-delay systems with algebraic constraints

Autor:	Chen, Yahao, Ghanes, Malek, Barbot, Jean-Pierre
Rok vydání:	2022
Předmět:	Electrical Engineering and Systems Science - Systems and Control Mathematics - Optimization and Control 34A09 34K32
Druh dokumentu:	Working Paper
Popis:	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. Comment: 8 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.10321 Zobrazit plný text záznamu View this record from Arxiv