Title data
Li, Huijuan ; Baier, Robert ; Grüne, Lars ; Hafstein, Sigurdur Freyr ; Wirth, Fabian:
Computation of local ISS Lyapunov functions with low gains via linear programming.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2015
.  19 p.
There is a more recent version of this item available. 
Project information
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Abstract in another language
In this paper, we present a numerical algorithm for computing ISS Lyapunov functions for continuoustime systems which are 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. The objective of the linear programming problem is to minimize the gain. We show that for every ISS system with a locally Lipschitz righthand side our algorithm is in principle able to deliver an ISS Lyapunov function. For $C^2$ righthand sides a more efficient algorithm is proposed.
Further data
Item Type:  Preprint, postprint, working paper, discussion paper 

Additional notes:  Contents:
1. Introduction, 2. Notations and Preliminaries, 3. The algorithm, 3.1 Definitions, 3.2 Interpolation errors, 3.3 The Algorithm, 4. Main results, 5. Examples, 6. Conclusions, 7. Acknowledgement. accepted for publication in DCDSB vol. 20, no. 8 (2015) 
Keywords:  nonlinear systems; local inputtostate stability; local ISS Lyapunov function; robust Lyapunov function; linear programming 
Subject classification:  Mathematics Subject Classification Code: 37B25 93D09 93D30 (34D20 90C05 
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 
Result of work at the UBT:  Yes 
DDC Subjects:  500 Science > 510 Mathematics 
Date Deposited:  14 Feb 2015 22:00 
Last Modified:  24 Jul 2015 10:25 
URI:  https://eref.unibayreuth.de/id/eprint/6988 
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 Computation of local ISS Lyapunov functions with low gains via linear programming. (deposited 14 Feb 2015 22:00) [Currently Displayed]