Peter Giesl 5-Aceepted-4.11.20.pdf (8.79 MB)
System specific triangulations for the construction of CPA lyapunov functions
journal contribution
posted on 2023-06-09, 22:06 authored by Peter GieslPeter Giesl, Sigurdur HafsteinRecently, 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 affine) 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.
History
Publication status
- Published
File Version
- Accepted version
Journal
Discrete and Continuous Dynamical Systems Series B: a journal bridging mathematics and sciencesISSN
1531-3492Publisher
American Institute of Mathematical SciencesExternal DOI
Page range
1-20Pages
21.0Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2020-11-10First Open Access (FOA) Date
2022-01-01First Compliant Deposit (FCD) Date
2020-11-09Usage metrics
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