# Iterative Construction of Complete Lyapunov Functions

### Carlos Argáez, Peter Giesl, Sigurdur Hafstein

#### Abstract

Dynamical systems describe the evolution of quantities governed by differential equations. Hence, they represent a very powerful prediction tool in many disciplines such as physics and engineering, chemistry and biology and even in economics, among others. Their importance relies on their capability of predicting, as a function of time, future states of the corresponding system under consideration by means of the current, known state. Many difficulties arise when trying to solve such systems. Complete Lyapunov functions allow for the systematic study of complicated dynamical systems. In this paper, we present a new iterative algorithm that avoids obtaining trivial solutions when constructing complete Lyapunov functions. This algorithm is based on mesh-free numerical approximation and analyzes the failure of convergence in certain areas to determine the chain-recurrent set.

Download#### Paper Citation

#### in Harvard Style

Argáez C., Giesl P. and Hafstein S. (2018). **Iterative Construction of Complete Lyapunov Functions**.In *Proceedings of 8th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,* ISBN 978-989-758-323-0, pages 211-222. DOI: 10.5220/0006835402110222

#### in Bibtex Style

@conference{simultech18,

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

title={Iterative Construction of Complete Lyapunov Functions},

booktitle={Proceedings of 8th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},

year={2018},

pages={211-222},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006835402110222},

isbn={978-989-758-323-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of 8th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,

TI - Iterative Construction of Complete Lyapunov Functions

SN - 978-989-758-323-0

AU - Argáez C.

AU - Giesl P.

AU - Hafstein S.

PY - 2018

SP - 211

EP - 222

DO - 10.5220/0006835402110222