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For a class of smooth nonlinear multivariable systems whose working-points vary with time and which may be represented by a linear MIMO ARX model at each working-point, a combination of a local linearization and a polytopic uncertain linear parameter-varying (LPV) state-space model are built to approximate the present and the future system's nonlinear behavior respectively. The combination models are constructed on the basis of a matrix polynomial MIMO RBF-ARX model identified offline for characterizing the underlying nonlinear system. A min-max robust MPC strategy is investigated for the systems based on the approximate models proposed. The closed loop stability of the MPC algorithm is guaranteed by the use of time-varying parameter-dependent Lyapunov function and the feasibility of the linear matrix inequalities (LMIs). The effectiveness of the modeling and control methods proposed in this paper is illustrated by a case study of a thermal power plant simulator.