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Automatic determination of connected sublevel sets of CPA Lyapunov functions
journal contribution
posted on 2023-06-09, 20:14 authored by Peter GieslPeter Giesl, Conor Osborne, Sigurdur HafsteinLyapunov functions are an important tool to determine the basin of attraction of equilibria. In particular, the connected component of a sublevel set, which contains the equilibrium, is a forward invariant subset of the basin of attraction. One method to compute a Lyapunov function for a general nonlinear autonomous differential equation constructs a Lyapunov function, which is continuous and piecewise affine (CPA) on each simplex of a fixed triangulation. In this paper we propose an algorithm to determine the largest connected sublevel set of such a CPA Lyapunov function and prove that it determines the largest subset of the basin of attraction that can be obtained by this Lyapunov function.
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Publication status
- Published
File Version
- Accepted version
Journal
SIAM Journal on Applied Dynamical Systems (SIADS)ISSN
1536-0040Publisher
Society for Industrial and Applied MathematicsExternal DOI
Issue
2Volume
19Page range
1029-1056Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2020-01-14First Open Access (FOA) Date
2020-05-05First Compliant Deposit (FCD) Date
2020-01-13Usage metrics
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