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Input-to-state dynamical stability and its Lyapunov function characterization

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005495
URN to cite this document: urn:nbn:de:bvb:703-epub-5495-0

Title data

Grüne, Lars:
Input-to-state dynamical stability and its Lyapunov function characterization.
Bayreuth , 2002

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Abstract

We present a new variant of the input-to-state stability (ISS) property which is based on using a one-dimensional dynamical system for building the class KL function for the decay estimate and for describing the influence of the perturbation. We show the relation to the original ISS formulation and describe characterizations by means of suitable Lyapunov functions. As applications, we derive quantitative results on stability margins for nonlinear systems and a quantitative version of a small gain theorem for nonlinear systems.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): The preprint that was available until January 25, 2002 (carrying the date May 16, 2001) had a systematic typo in several formulas:
Each inequality of the type
DV(x)f(x,u) <= -g(x) (like, e.g., in formula (3.4))
has to be replaced by
DV(x)f(x,u) <= -g(V(x))
This error was due to multiple copying and pasting an erroneous formula and has no impact on the proofs and results in this paper, except for some minor changes in the statement and proof of Theorem 3.3.

erschienen In:
IEEE Transactions on Automatic Control. Bd. 47 (2002) Heft 9 . - S. 1499-1504
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-5495-0
Date Deposited: 12 May 2021 06:23
Last Modified: 12 May 2021 06:23
URI: https://epub.uni-bayreuth.de/id/eprint/5495

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