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Author: Sigurdur Freyr Hafstein

Affiliation: University of Iceland, Iceland

ISBN: 978-989-758-265-3

Keyword(s): Simplicial Complex, Triangulation, Algorithm, Lyapunov Function, Nonlinear System, Discrete-time System.

Related Ontology Subjects/Areas/Topics: Formal Methods ; Mathematical Simulation ; Non-Linear Systems ; Optimization Issues ; Performance Analysis ; Simulation and Modeling ; Simulation Tools and Platforms

Abstract: Several algorithms have been suggested to parameterize continuous and piecewise affine Lyapunov functions for nonlinear systems in various settings. In these algorithms linear constraints are formulated for the values of a Lyapunov function at all vertices of a simplicial complex. They are then either solved using convex optimization or computed by other means and then verified. Originally these algorithms were designed for continuous-time systems and their adaptation to discrete-time systems and control systems poses some challenges in designing and implementing efficient algorithms and data structures for simplicial complexes. In this paper we discuss several of these and give efficient implementations in C++

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Paper citation in several formats:
Freyr Hafstein S. (2017). Efficient Algorithms for Simplicial Complexes Used in the Computation of Lyapunov Functions for Nonlinear Systems.In Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, ISBN 978-989-758-265-3, pages 398-409. DOI: 10.5220/0006480003980409

@conference{simultech17,
author={Sigurdur Freyr Hafstein},
title={Efficient Algorithms for Simplicial Complexes Used in the Computation of Lyapunov Functions for Nonlinear Systems},
booktitle={Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},
year={2017},
pages={398-409},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006480003980409},
isbn={978-989-758-265-3},
}

TY - CONF

JO - Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,
TI - Efficient Algorithms for Simplicial Complexes Used in the Computation of Lyapunov Functions for Nonlinear Systems
SN - 978-989-758-265-3
AU - Freyr Hafstein S.
PY - 2017
SP - 398
EP - 409
DO - 10.5220/0006480003980409

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