# Efficient Verification of CPA Lyapunov Functions

### Sigurdur Hafstein

#### 2022

#### Abstract

Lyapunov functions can be used to characterize the stability and basins of attraction for dynamical systems, whose dynamics are defined by ordinary differential equations. Since the analytic generation of Lyapunov functions for nonlinear systems is a formidable task, one often resorts to numerical methods. In this paper we study the efficient verification of the conditions for a Lyapunov function using affine interpolation over a triangulation; the values of the Lyapunov function candidate at the vertices of the triangulation can be generated using various different formulas from converse theorems in the Lyapunov stability theory. Further, we give an implementation in C++ and demonstrate its efficiency and applicability.

Download#### Paper Citation

#### in Harvard Style

Hafstein S. (2022). **Efficient Verification of CPA Lyapunov Functions**. In *Proceedings of the 19th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-989-758-585-2, pages 120-129. DOI: 10.5220/0011231700003271

#### in Bibtex Style

@conference{icinco22,

author={Sigurdur Hafstein},

title={Efficient Verification of CPA Lyapunov Functions},

booktitle={Proceedings of the 19th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2022},

pages={120-129},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0011231700003271},

isbn={978-989-758-585-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 19th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - Efficient Verification of CPA Lyapunov Functions

SN - 978-989-758-585-2

AU - Hafstein S.

PY - 2022

SP - 120

EP - 129

DO - 10.5220/0011231700003271