Title data
Li, Huijuan ; Baier, Robert ; Grüne, Lars ; Hafstein, Sigurdur Freyr ; Wirth, Fabian:
Computation of local ISS Lyapunov functions via linear programming.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2014
.  7 S.


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Project financing: 
Andere European Union "FP7PeopleITN" programme 
Abstract
In this paper, we present a numerical algorithm for computing a local ISS Lyapunov function for systems which are locally inputtostate stable (ISS) on compact subsets of the state space. The algorithm relies on a linear programming problem and computes a continuous, piecewise affine ISS Lyapunov function on a simplicial grid covering the given compact set excluding a small neighborhood of the origin. We show that the ISS Lyapunov function delivered by the algorithm is a viscosity subsolution of a partial differential equation.
Further data
Item Type:  Preprint, postprint 

Additional notes (visible to public):  Contents:
I. Introduction, II. Notations and preliminaries, III. The algorithm, III.A Definitions, III.B Interpolation errors, III.C The algorithm, IV. Main result. © 2014 IEEE. Reuse of this content is subject to the IEEE Copyright. This content will be published in: Proceedings on the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), July 7–11, 2014, University of Groningen, Groningen, Netherlands, check the forthcoming abstract in IEEE Explore. 
Keywords:  nonlinear systems; local inputtostate stability; local ISS Lyapunov function; linear programming; viscosity subsolution 
Subject classification:  Mathematics Subject Classification Code: 93D30 (34D20 93C10) 
DDC Subjects:  500 Science > 510 Mathematics 
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 Profile Fields Profile Fields > Advanced Fields Profile Fields > Advanced Fields > Nonlinear Dynamics 
Language:  English 
Originates at UBT:  Yes 
URN:  urn:nbn:de:bvb:703epub18803 
Date Deposited:  11 Feb 2015 11:49 
Last Modified:  28 Mar 2019 11:03 
URI:  https://epub.unibayreuth.de/id/eprint/1880 