Automatic determination of connected sublevel sets of CPA lyapunov functions

Peter Gies, Conor Osborne, Sigurdur Hafstein

Rannsóknarafurð: Framlag til fræðitímaritsGreinritrýni

Útdráttur

Lyapunov 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.

Upprunalegt tungumálEnska
Síður (frá-til)1029-1056
Síðufjöldi28
FræðitímaritSIAM Journal on Applied Dynamical Systems
Bindi19
Númer tölublaðs2
DOI
ÚtgáfustaðaÚtgefið - 2020

Athugasemd

Publisher Copyright:
© 2020 Society for Industrial and Applied Mathematics.

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