  In this paper we propose a convex programming based method for computing
robust regions of attraction for state-constrained perturbed discrete-time
polynomial systems. The robust region of attraction of interest is a set of
states such that every possible trajectory initialized in it will approach an
equilibrium state while never violating the specified state constraint,
regardless of the actual perturbation. Based on a Bellman equation which
characterizes the interior of the maximal robust region of attraction as the
strict one sub-level set of its unique bounded and continuous solution, we
construct a semi-definite program for computing robust regions of attraction.
Under appropriate assumptions, 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 and converge to the
interior of the maximal robust region of attraction in measure. Finally, we
demonstrate the method by two examples.
