# Evaluation of Lyapunov Function Candidates through Averaging Iterations

### Carlos Argáez, Peter Giesl, Sigurdur Hafstein

#### 2020

#### Abstract

A complete Lyapunov function determines the behaviour of a dynamical system. In particular, it splits the phase space into the chain-recurrent set, where solutions show (almost) repetitive behaviour, and the part exhibiting gradient-like flow where the dynamics are transient. Moreover, it reveals the stability of sets and basins of attraction through its sublevel sets. In this paper, we combine two previous methods to compute complete Lyapunov functions: we employ quadratic optimization with equality and inequality constraints to compute a complete Lyapunov function candidate and we evaluate its quality by using a method that improves approximations of complete Lyapunov function candidates through iterations.

Download#### Paper Citation

#### in Harvard Style

Argáez C., Giesl P. and Hafstein S. (2020). **Evaluation of Lyapunov Function Candidates through Averaging Iterations**.In *Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-989-758-442-8, pages 734-744. DOI: 10.5220/0009992507340744

#### in Bibtex Style

@conference{icinco20,

author={Carlos Argáez and Peter Giesl and Sigurdur Hafstein},

title={Evaluation of Lyapunov Function Candidates through Averaging Iterations},

booktitle={Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2020},

pages={734-744},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0009992507340744},

isbn={978-989-758-442-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - Evaluation of Lyapunov Function Candidates through Averaging Iterations

SN - 978-989-758-442-8

AU - Argáez C.

AU - Giesl P.

AU - Hafstein S.

PY - 2020

SP - 734

EP - 744

DO - 10.5220/0009992507340744