Verifying Positivity of Piecewise Quadratic Lyapunov Functions

Sigurdur Hafstein, Eggert Hafsteinsson

2025

Abstract

Continuous, piecewise quadratic (CPQ) Lyapunov functions are frequently used to assert stability for switched, cone-wise linear systems. It is advantageous to construct such Lyapunov functions in two steps: first a function is parameterized that is decreasing along all system trajectories, then it is verified whether this function is positive definite. Usually these steps have been performed using linear matrix inequalities (LMIs), but recently a linear programming (LP) approach for the first step has been suggested. In this paper we present a new algorithm to verify the positivity of CPQ Lyapunov function candidates, parameterized either with LMIs or LP. Further, we prove that the algorithm is non-conservative and will always be able to either assert positive definiteness of a CPQ Lyapunov function candidate or find a point where it is negative.

Paper Citation

in Harvard Style

Hafstein S. and Hafsteinsson E. (2025). Verifying Positivity of Piecewise Quadratic Lyapunov Functions. In Proceedings of the 22nd International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO; ISBN 978-989-758-770-2, SciTePress, pages 435-444. DOI: 10.5220/0013713600003982

in Bibtex Style

@conference{icinco25,
author={Sigurdur Hafstein and Eggert Hafsteinsson},
title={Verifying Positivity of Piecewise Quadratic Lyapunov Functions},
booktitle={Proceedings of the 22nd International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO},
year={2025},
pages={435-444},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013713600003982},
isbn={978-989-758-770-2},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 22nd International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO
TI - Verifying Positivity of Piecewise Quadratic Lyapunov Functions
SN - 978-989-758-770-2
AU - Hafstein S.
AU - Hafsteinsson E.
PY - 2025
SP - 435
EP - 444
DO - 10.5220/0013713600003982
PB - SciTePress