2018/12/27 by Xue, Bai, Wang, Qiuye, Zhan, Naijun +2 · 1 citation
#FOS: Electrical engineering #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.1812.10588
In this paper we propose a novel semi-definite 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 semi-definite program is guaranteed and there exists a sequence of solutions such that their strict one sub-level 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.