CPA Lyapunov Functions: Switched Systems vs. Differential Inclusions

Sigurdur Hafstein

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Paper

CPA Lyapunov Functions: Switched Systems vs. Differential Inclusions

Topics: Nonlinear Signals and Systems

In Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics ICINCO - Volume 1, 745-753, 2020

Author: Sigurdur Hafstein

Affiliation: Science Institute and Faculty of Physical Sciences, University of Iceland, Dunhagi 5, 107 Reykjavík, Iceland

Keyword(s): Lyapunov Function, Switched Systems, Differential Inclusions, Numerical Algorithm, Artstein’s Circles.

Abstract: We present an algorithm that uses linear programming to parameterize continuous and piecewise affine Lyapunov functions for switched systems. The novel feature of the algorithm is, that it can compute Lyapunov functions for switched system with a strongly asymptotically stable equilibrium, for which the equilibrium of the corresponding differential inclusion is merely weakly asymptotically stable. For the differential inclusion no such Lyapunov function exists. This is achieved by removing constraints from a linear programming problem of an earlier algorithm to compute Lyapunov functions, that are not necessary to assert strong stability for the switched system. We demonstrate the benefits of this new algorithm sing Artstein’s circles as an example.

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Paper citation in several formats:

Hafstein, S. (2020). CPA Lyapunov Functions: Switched Systems vs. Differential Inclusions. In Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics - ICINCO; ISBN 978-989-758-442-8; ISSN 2184-2809, SciTePress, pages 745-753. DOI: 10.5220/0009992707450753

@conference{icinco20,
author={Sigurdur Hafstein.},
title={CPA Lyapunov Functions: Switched Systems vs. Differential Inclusions},
booktitle={Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics - ICINCO},
year={2020},
pages={745-753},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0009992707450753},
isbn={978-989-758-442-8},
issn={2184-2809},
}

TY - CONF

JO - Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics - ICINCO
TI - CPA Lyapunov Functions: Switched Systems vs. Differential Inclusions
SN - 978-989-758-442-8
IS - 2184-2809
AU - Hafstein, S.
PY - 2020
SP - 745
EP - 753
DO - 10.5220/0009992707450753
PB - SciTePress