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

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.
In: Systems & Control Letters. Vol. 38 (October 1999) Issue 2 . - pp. 127-134.
ISSN 1872-7956
DOI: https://doi.org/10.1016/S0167-6911(99)00053-5

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Abstract in another language

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: Article in a journal
Refereed: Yes
Keywords: Asymptotic stability; Exponential stability; Input-to-state stability; Nonlinear H∞
Institutions of the University: 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)
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
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 19 Feb 2021 07:30
Last Modified: 06 May 2021 11:45
URI: https://eref.uni-bayreuth.de/id/eprint/63216