Interval-driven discrete-time general nonlinear robust control: stabilization with closed-loop robust DOA enlargement

Abstract: This paper presents new results that allow one to address the discrete-time general nonlinear robust control problem. The uncertain system is described by a general nonlinear function set characterized by the nominal model and the corresponding modeling error bound. Traditional synthesis methods design parameters of a structured robust controller. The key aim of this paper is to find an unstructured robust controller set in the state-control space, which enlarges the estimate of the closed-loop robust domain of attraction (RDOA). Based on the interval analysis arithmetic, a numerical method to estimate the unstructured robust controller set is proposed and the rigorous convergence analysis is given. The existing RDOA results are constrained by the level-set of the Lyapunov function, whereas the results in this paper remove this limitation. Furthermore, a solvable optimization problem is formulated so the estimate of RDOA is enlarged by selecting a Lyapunov function from a Lyapunov function set of sum-of-squares polynomials. The method is then validated by a specific case simulation study and results show more extensive RDOA than the previous methods.