  In this paper, the stabilization problem with closed-loop domain of
attraction (DOA) enlargement for discrete-time general nonlinear plants is
solved. First, a sufficient condition for asymptotic stabilization and
estimation of the closed-loop DOA is given. It shows that, for a given Lyapunov
function, the negative-definite and invariant set in the state-control space is
a stabilizing controller set and its projection along the control space to the
state space can be an estimate of the closed-loop DOA. Then, an algorithm is
proposed to approximate the negative-definite and invariant set for the given
Lyapunov function, in which an interval analysis algorithm is used to find an
inner approximation of sets as precise as desired. Finally, a solvable
optimization problem is formulated to enlarge the estimate of the closed-loop
DOA by selecting an appropriate Lyapunov function from a positive-definite
function set. The proposed method try to find a unstructured controller set
(namely, the negative-definite and invariant set) in the state-control space
rather than design parameters of a structured controller in traditional
synthesis methods.
