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Nonlinear robust control is pursued by overcoming the drawback of linearrobust control that it ignores available information about existingnonlinearities and the resulting controllers may be too conservative,especially when the nonlinearities are significant. However, most existingnonlinear robust control approaches just consider the affine nonlinear nominalmodel and thereby ignore available information about existing non-affinenonlinearities. When the general nonlinear nominal model is considered, therobust domain of attraction (RDOA) of closed-loops requires extensiveinvestigation because it is hard to achieve the global stabilization. In thispaper, we propose a new nonlinear robust control method based on Lyapunovfunction to stabilize a discrete-time uncertain system and to estimate the RDOAof closed-loops. First, a sufficient condition for robust stabilization of allplants in a plant set and estimation of the RDOA of all closed-loops isproposed. Then, to tackle the non-affine nonlinearities, a data-driven methodof estimating the robust negative-definite domains (RNDD) is presented, andbased on it the estimation of the RDOA of closed-loops and the resultingcontroller design are also given.

Data-Driven Robust Stabilization with RobustDomain of Attraction Estimate for Nonlinear Discrete-Time Systems