SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1029-1056, January 2020.
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.

中文翻译：

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自动确定CPA Lyapunov函数的关联子级集

SIAM应用动力系统杂志，第19卷，第2期，第1029-1056页，2020年1月。Lyapunov
函数是确定均衡吸引基础的重要工具。特别是，包含平衡的子级集的连通分量是吸引盆地的前向不变子集。计算一般非线性自治微分方程的Lyapunov函数的一种方法是构造Lyapunov函数，该函数在固定三角剖分的每个单形上是连续且分段仿射（CPA）。在本文中，我们提出了一种算法来确定这种CPA Lyapunov函数的最大连通子级集，并证明它确定了可以通过该Lyapunov函数获得的吸引盆地的最大子集。