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Most of nonlinear robust control methods just consider the affine nonlinearnominal model. When the nominal model is assumed to be affine nonlinear,available information about existing non-affine nonlinearities is ignored. Fornon-affine nonlinear system, Li et al. (2019) proposes a new nonlinear controlmethod to solve the robust stabilization problem with estimation of the robustclosed-loop DOA (Domain of attraction). However, Li et al. (2019) assumes thatthe Lyapunov function is given and does not consider the problem of finding agood Lyapunov function to enlarge the estimate of the robust closed-loop DOA.The motivation of this paper is to enlarge the estimate of the closed-loop DOAby selecting an appropriate Lyapunov function. To achieve this goal, a solvableoptimization problem is formulated to select an appropriate Lyapunov functionfrom a parameterized positive-definite function set. The effectiveness ofproposed method is verified by numerical results.

Data-Driven Robust Stabilization with Robust DOA Enlargement for Nonlinear Systems