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.
Original languageEnglish
Title of host publicationMathematical Control Theory I
EditorsM. Kanat Camlibel, R.P. Ramkrishna Pasumarthy, A. Agung Julius, Jacquelien M.A. Scherpen
Place of PublicationLondon
PublisherSpringer
Pages343-348
Number of pages6
ISBN (Print)978-3-319-20987-6
DOIs
Publication statusPublished - 14 Jul 2015

Publication series

NameLecture Notes in Control and Information Sciences
PublisherSpringer Verlag
Number461
Volume461
ISSN (Print)0170-8643

Fingerprint

Infinite-dimensional Systems
Linearization
Linear Systems
Local Stability
Exponential Stability
Asymptotic Stability
Lyapunov Function
Nonlinear Systems
Imply

Keywords

  • MSC-53C38
  • MSC-34H05
  • METIS-314962
  • IR-98399
  • EWI-26283

Cite this

Zwart, H. J. (2015). Examples on Stability for Infinite-Dimensional Systems. In M. Kanat Camlibel, R. P. Ramkrishna Pasumarthy, A. Agung Julius, & J. M. A. Scherpen (Eds.), Mathematical Control Theory I (pp. 343-348). (Lecture Notes in Control and Information Sciences; Vol. 461, No. 461). London: Springer. https://doi.org/10.1007/978-3-319-20988-3_18
Zwart, Heiko J. / Examples on Stability for Infinite-Dimensional Systems. Mathematical Control Theory I. editor / M. Kanat Camlibel ; R.P. Ramkrishna Pasumarthy ; A. Agung Julius ; Jacquelien M.A. Scherpen. London : Springer, 2015. pp. 343-348 (Lecture Notes in Control and Information Sciences; 461).
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Zwart, HJ 2015, Examples on Stability for Infinite-Dimensional Systems. in M Kanat Camlibel, RP Ramkrishna Pasumarthy, A Agung Julius & JMA Scherpen (eds), Mathematical Control Theory I. Lecture Notes in Control and Information Sciences, no. 461, vol. 461, Springer, London, pp. 343-348. https://doi.org/10.1007/978-3-319-20988-3_18

Examples on Stability for Infinite-Dimensional Systems. / Zwart, Heiko J.

Mathematical Control Theory I. ed. / M. Kanat Camlibel; R.P. Ramkrishna Pasumarthy; A. Agung Julius; Jacquelien M.A. Scherpen. London : Springer, 2015. p. 343-348 (Lecture Notes in Control and Information Sciences; Vol. 461, No. 461).

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

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KW - MSC-53C38

KW - MSC-34H05

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KW - IR-98399

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Zwart HJ. Examples on Stability for Infinite-Dimensional Systems. In Kanat Camlibel M, Ramkrishna Pasumarthy RP, Agung Julius A, Scherpen JMA, editors, Mathematical Control Theory I. London: Springer. 2015. p. 343-348. (Lecture Notes in Control and Information Sciences; 461). https://doi.org/10.1007/978-3-319-20988-3_18