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Asymptotic stability equals exponential stability, and ISS equals finite energy gain - if you twist your eyes

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005456
URN to cite this document: urn:nbn:de:bvb:703-epub-5456-9

Title data

Grüne, Lars ; Sontag, Eduardo D. ; Wirth, Fabian R.:
Asymptotic stability equals exponential stability, and ISS equals finite energy gain - if you twist your eyes.
Bayreuth , 1999

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Abstract

In this paper we show that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables. The same is shown for input-to-state stability and input-to-state exponential stability, and for input-to-state exponential stability and a nonlinear H∞ estimate.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): erschienen In:
Systems & Control Letters. Bd. 38 (Oktober 1999) Heft 2 . - S. 127-134
Keywords: Asymptotic stability; Exponential stability; Input-to-state stability; Nonlinear H∞
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-5456-9
Date Deposited: 06 May 2021 11:44
Last Modified: 06 May 2021 11:44
URI: https://epub.uni-bayreuth.de/id/eprint/5456

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