System specific triangulations for the construction of cpa lyapunov functions

Peter Giesl, Sigurdur Hafstein

Rannsóknarafurð: Framlag til fræðitímaritsGreinritrýni

Útdráttur

Recently, a transformation of the vertices of a regular triangulation of Rn with vertices in the lattice Zn was introduced, which distributes the vertices with approximate rotational symmetry properties around the origin. We prove that the simplices of the transformed triangulation are (h; d)-bounded, a type of non-degeneracy particularly useful in the numerical computation of Lyapunov functions for nonlinear systems using the CPA (continuous piecewise afine) method. Additionally, we discuss and give examples of how this transformed triangulation can be used together with a Lyapunov function for a linearization to compute a Lyapunov function for a nonlinear system with the CPA method using considerably fewer simplices than when using a regular triangulation.

Upprunalegt tungumálEnska
Síður (frá-til)6027-6046
Síðufjöldi20
FræðitímaritDiscrete and Continuous Dynamical Systems - Series B
Bindi26
Númer tölublaðs12
DOI
ÚtgáfustaðaÚtgefið - des. 2021

Athugasemd

Funding Information:
2020 Mathematics Subject Classification. Primary: 93D30, 51M20, 37N30; Secondary: 65D05. Key words and phrases. Triangulation, Lyapunov function, nonlinear transformation, simplicial complex. The research in this paper was partly supported by the Icelandic Research Fund (Rannís) grant number 163074-052, Complete Lyapunov functions: Efficient numerical computation.

Publisher Copyright:
© 2021 American Institute of Mathematical Sciences. All rights reserved.

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