In this note the Extended Lie bracket operator is introduced for the analysis and control of nonlinear time-delay systems (NLTDS). This tool is used to characterize the integrability conditions of a given submodule. The obtained results have two fundamental outcomes. First, they define the necessary and sufficient conditions under which a given set of nonlinear one-forms in the n-dimensional delayed variables x(t), ... , x (t - sD), with D constant but unknown, are integrable, thus generalizing the well known fundamental Frobenius Theorem to delay systems. Secondly, they set the basis for the extension to this context of the geometric approach used for delay-free systems. The effectiveness of the results is shown by solving the problem of the equivalence of a NLTDS to an accessible Linear Time-Delay System (LTDS) by bicausal change of coordinates.

Extended Lie Brackets for Nonlinear Time-Delay Systems / Califano, Claudia; Luis Alejandro Marquez, Martinez; Claude H., Moog. - In: IEEE TRANSACTIONS ON AUTOMATIC CONTROL. - ISSN 0018-9286. - 56:9(2011), pp. 2213-2218. [10.1109/tac.2011.2157405]

Extended Lie Brackets for Nonlinear Time-Delay Systems

CALIFANO, Claudia;
2011

Abstract

In this note the Extended Lie bracket operator is introduced for the analysis and control of nonlinear time-delay systems (NLTDS). This tool is used to characterize the integrability conditions of a given submodule. The obtained results have two fundamental outcomes. First, they define the necessary and sufficient conditions under which a given set of nonlinear one-forms in the n-dimensional delayed variables x(t), ... , x (t - sD), with D constant but unknown, are integrable, thus generalizing the well known fundamental Frobenius Theorem to delay systems. Secondly, they set the basis for the extension to this context of the geometric approach used for delay-free systems. The effectiveness of the results is shown by solving the problem of the equivalence of a NLTDS to an accessible Linear Time-Delay System (LTDS) by bicausal change of coordinates.
2011
nonlinear continuous-time systems; geometric approach; linear equivalence; delay systems; nonlinear continuous-time systems.
01 Pubblicazione su rivista::01a Articolo in rivista
Extended Lie Brackets for Nonlinear Time-Delay Systems / Califano, Claudia; Luis Alejandro Marquez, Martinez; Claude H., Moog. - In: IEEE TRANSACTIONS ON AUTOMATIC CONTROL. - ISSN 0018-9286. - 56:9(2011), pp. 2213-2218. [10.1109/tac.2011.2157405]
File allegati a questo prodotto
File Dimensione Formato  
VE_2011_11573-380007.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 295.57 kB
Formato Adobe PDF
295.57 kB Adobe PDF   Contatta l'autore

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/380007
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 31
  • ???jsp.display-item.citation.isi??? 28
social impact