Examples on stability for infinite-dimensional systems

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

Abstract

By means of examples, we study stability of infinite-dimensional linear and nonlinear systems. First we show that having a (strict) Lyapunov function does not imply asymptotic stability, even not for linear systems. Second, we show that to conclude (local) exponential stability from the linearization, care must be taken how the linearization is obtained.

LanguageEnglish
Title of host publicationMathematical Control Theory I : Nonlinear and Hybrid Control Systems
EditorsM.K. Camlibel, A.A. Julius, R. Pasumarthy, J.M.A. Scherpen
Place of PublicationDordrecht
PublisherSpringer
Pages343-348
Number of pages6
ISBN (Electronic)978-3-319-20988-3
ISBN (Print)978-3-319-20987-6
DOIs
StatePublished - 2015
EventWorkshop on Mathematical Systems Theory: From Behaviors to Nonlinear Control, 12-13 July 2015, Groningen, The Netherlands - Jan C. Willems Center for Systems and Control at the University of Groningen, Groningen, Netherlands
Duration: 12 Jul 201513 Jul 2015

Publication series

NameLecture Notes in Control and Information Sciences
Volume461
ISSN (Print)0170-8643

Conference

ConferenceWorkshop on Mathematical Systems Theory: From Behaviors to Nonlinear Control, 12-13 July 2015, Groningen, The Netherlands
CountryNetherlands
CityGroningen
Period12/07/1513/07/15

Cite this

Zwart, H. J. (2015). Examples on stability for infinite-dimensional systems. In M. K. Camlibel, A. A. Julius, R. Pasumarthy, & J. M. A. Scherpen (Eds.), Mathematical Control Theory I : Nonlinear and Hybrid Control Systems (pp. 343-348). (Lecture Notes in Control and Information Sciences; Vol. 461). Dordrecht: Springer. DOI: 10.1007/978-3-319-20988-3_18
Zwart, H.J./ Examples on stability for infinite-dimensional systems. Mathematical Control Theory I : Nonlinear and Hybrid Control Systems. editor / M.K. Camlibel ; A.A. Julius ; R. Pasumarthy ; J.M.A. Scherpen. Dordrecht : Springer, 2015. pp. 343-348 (Lecture Notes in Control and Information Sciences).
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Zwart, HJ 2015, Examples on stability for infinite-dimensional systems. in MK Camlibel, AA Julius, R Pasumarthy & JMA Scherpen (eds), Mathematical Control Theory I : Nonlinear and Hybrid Control Systems. Lecture Notes in Control and Information Sciences, vol. 461, Springer, Dordrecht, pp. 343-348, Workshop on Mathematical Systems Theory: From Behaviors to Nonlinear Control, 12-13 July 2015, Groningen, The Netherlands, Groningen, Netherlands, 12/07/15. DOI: 10.1007/978-3-319-20988-3_18

Examples on stability for infinite-dimensional systems. / Zwart, H.J.

Mathematical Control Theory I : Nonlinear and Hybrid Control Systems. ed. / M.K. Camlibel; A.A. Julius; R. Pasumarthy; J.M.A. Scherpen. Dordrecht : Springer, 2015. p. 343-348 (Lecture Notes in Control and Information Sciences; Vol. 461).

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

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Zwart HJ. Examples on stability for infinite-dimensional systems. In Camlibel MK, Julius AA, Pasumarthy R, Scherpen JMA, editors, Mathematical Control Theory I : Nonlinear and Hybrid Control Systems. Dordrecht: Springer. 2015. p. 343-348. (Lecture Notes in Control and Information Sciences). Available from, DOI: 10.1007/978-3-319-20988-3_18