Convergent systems: nonlinear simplicity

A. Pavlov, N. van de Wouw

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

1 Citation (Scopus)

Abstract

Convergent systems are systems that have a uniquely defined globally asymptotically stable steady-state solution. Asymptotically stable linear systems excited by a bounded time varying signal are convergent. Together with the superposition principle, the convergence property forms a foundation for a large number of analysis and (control) design tools for linear systems. Nonlinear convergent systems are in many ways similar to linear systems and are, therefore, in a certain sense simple, although the superposition principle does not hold. This simplicity allows one to solve a number of analysis and design problems for nonlinear systems and makes the convergence property highly instrumental for practical applications. In this chapter, we review the notion of convergent systems and its applications to various analyses and design problems within the field of systems and control.

LanguageEnglish
Title of host publicationNonlinear systems
Subtitle of host publicationtechniques for dynamical analysis and control
EditorsN. Wouw, van de, E. Lefeber, I. Lopez Arteaga
Place of PublicationBerlin
PublisherSpringer
Pages51-77
Number of pages27
ISBN (Print)9783319303567
DOIs
StatePublished - 2017
EventInternational workshop on Nonlinear Systems in honor of Henk Nijmeijer’s 60th birthday, 2016 - Eindhoven, Netherlands
Duration: 21 Jan 201621 Jan 2016

Publication series

NameLecture Notes in Control and Information Sciences
Volume470
ISSN (Print)01708643

Conference

ConferenceInternational workshop on Nonlinear Systems in honor of Henk Nijmeijer’s 60th birthday, 2016
CountryNetherlands
CityEindhoven
Period21/01/1621/01/16

Fingerprint

time

Cite this

Pavlov, A., & van de Wouw, N. (2017). Convergent systems: nonlinear simplicity. In N. Wouw, van de, E. Lefeber, & I. Lopez Arteaga (Eds.), Nonlinear systems: techniques for dynamical analysis and control (pp. 51-77). (Lecture Notes in Control and Information Sciences; Vol. 470). Berlin: Springer. DOI: 10.1007/978-3-319-30357-4_3
Pavlov, A. ; van de Wouw, N./ Convergent systems : nonlinear simplicity. Nonlinear systems: techniques for dynamical analysis and control. editor / N. Wouw, van de ; E. Lefeber ; I. Lopez Arteaga. Berlin : Springer, 2017. pp. 51-77 (Lecture Notes in Control and Information Sciences).
@inbook{109903e6eb5b465b9a3cc00daea2982c,
title = "Convergent systems: nonlinear simplicity",
abstract = "Convergent systems are systems that have a uniquely defined globally asymptotically stable steady-state solution. Asymptotically stable linear systems excited by a bounded time varying signal are convergent. Together with the superposition principle, the convergence property forms a foundation for a large number of analysis and (control) design tools for linear systems. Nonlinear convergent systems are in many ways similar to linear systems and are, therefore, in a certain sense simple, although the superposition principle does not hold. This simplicity allows one to solve a number of analysis and design problems for nonlinear systems and makes the convergence property highly instrumental for practical applications. In this chapter, we review the notion of convergent systems and its applications to various analyses and design problems within the field of systems and control.",
author = "A. Pavlov and {van de Wouw}, N.",
year = "2017",
doi = "10.1007/978-3-319-30357-4_3",
language = "English",
isbn = "9783319303567",
series = "Lecture Notes in Control and Information Sciences",
publisher = "Springer",
pages = "51--77",
editor = "{Wouw, van de}, N. and E. Lefeber and {Lopez Arteaga}, I.",
booktitle = "Nonlinear systems",
address = "Germany",

}

Pavlov, A & van de Wouw, N 2017, Convergent systems: nonlinear simplicity. in N Wouw, van de, E Lefeber & I Lopez Arteaga (eds), Nonlinear systems: techniques for dynamical analysis and control. Lecture Notes in Control and Information Sciences, vol. 470, Springer, Berlin, pp. 51-77, International workshop on Nonlinear Systems in honor of Henk Nijmeijer’s 60th birthday, 2016, Eindhoven, Netherlands, 21/01/16. DOI: 10.1007/978-3-319-30357-4_3

Convergent systems : nonlinear simplicity. / Pavlov, A.; van de Wouw, N.

Nonlinear systems: techniques for dynamical analysis and control. ed. / N. Wouw, van de; E. Lefeber; I. Lopez Arteaga. Berlin : Springer, 2017. p. 51-77 (Lecture Notes in Control and Information Sciences; Vol. 470).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

TY - CHAP

T1 - Convergent systems

T2 - nonlinear simplicity

AU - Pavlov,A.

AU - van de Wouw,N.

PY - 2017

Y1 - 2017

N2 - Convergent systems are systems that have a uniquely defined globally asymptotically stable steady-state solution. Asymptotically stable linear systems excited by a bounded time varying signal are convergent. Together with the superposition principle, the convergence property forms a foundation for a large number of analysis and (control) design tools for linear systems. Nonlinear convergent systems are in many ways similar to linear systems and are, therefore, in a certain sense simple, although the superposition principle does not hold. This simplicity allows one to solve a number of analysis and design problems for nonlinear systems and makes the convergence property highly instrumental for practical applications. In this chapter, we review the notion of convergent systems and its applications to various analyses and design problems within the field of systems and control.

AB - Convergent systems are systems that have a uniquely defined globally asymptotically stable steady-state solution. Asymptotically stable linear systems excited by a bounded time varying signal are convergent. Together with the superposition principle, the convergence property forms a foundation for a large number of analysis and (control) design tools for linear systems. Nonlinear convergent systems are in many ways similar to linear systems and are, therefore, in a certain sense simple, although the superposition principle does not hold. This simplicity allows one to solve a number of analysis and design problems for nonlinear systems and makes the convergence property highly instrumental for practical applications. In this chapter, we review the notion of convergent systems and its applications to various analyses and design problems within the field of systems and control.

UR - http://www.scopus.com/inward/record.url?scp=84978524315&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-30357-4_3

DO - 10.1007/978-3-319-30357-4_3

M3 - Chapter

SN - 9783319303567

T3 - Lecture Notes in Control and Information Sciences

SP - 51

EP - 77

BT - Nonlinear systems

PB - Springer

CY - Berlin

ER -

Pavlov A, van de Wouw N. Convergent systems: nonlinear simplicity. In Wouw, van de N, Lefeber E, Lopez Arteaga I, editors, Nonlinear systems: techniques for dynamical analysis and control. Berlin: Springer. 2017. p. 51-77. (Lecture Notes in Control and Information Sciences). Available from, DOI: 10.1007/978-3-319-30357-4_3