SIAM Journal on Control and Optimization, Volume 59, Issue 2, Page 1083-1108, January 2021.
In this paper we propose a novel semidefinite programming based method to compute robust domains of attraction for state-constrained perturbed polynomial systems. A robust domain of attraction is a set of states such that every trajectory starting from it will approach an equilibrium while never violating a specified state constraint, regardless of the actual perturbation. The semi-definite program is constructed by relaxing a generalized Zubov's equation. The existence of solutions to the constructed semidefinite program is guaranteed, and there exists a sequence of solutions such that their strict one-sublevel sets inner-approximate the interior of the maximal robust domain of attraction in measure under appropriate assumptions. Some illustrative examples demonstrate the performance of our method.

中文翻译：

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合成状态约束摄动多项式系统的鲁棒吸引域

SIAM控制与优化杂志，第59卷，第2期，第1083-1108页，2021年1月
在本文中，我们提出了一种新颖的基于半定规划的方法，用于为状态受限的扰动多项式系统计算鲁棒的吸引域。一个强大的吸引域是一组状态，这样，从它开始的每个轨迹都将趋于平衡，而不会违反指定的状态约束，而与实际的扰动无关。通过放宽广义Zubov方程构造半定程序。保证了所构造的半定程序的解的存在，并且存在一系列的解，使得它们的严格的一个子级集在适当的假设下内部近似于度量的最大鲁棒吸引域的内部。一些说明性的例子说明了我们方法的性能。