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.