## 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 tungumál | Enska |
---|---|

Síður (frá-til) | 1029-1056 |

Síðufjöldi | 28 |

Fræðitímarit | SIAM Journal on Applied Dynamical Systems |

Bindi | 19 |

Númer tölublaðs | 2 |

DOI | |

Útgáfustaða | Útgefið - 2020 |

### Athugasemd

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