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1-D polynomial systems are generalization of conventional 1-D linear systems and can represent nonlinear control systems effectively. In this paper, conventional 2-D Roesser models are extended to that with polynomial system matrices, i.e. 2-D polynomial Roesser model. The problems of stability analysis and Hx control for 2-D polynomial Roesser model are considered in this paper. A sufficient condition for the stability of 2-D polynomial Roesser model is proposed and an Hx polynomial controller is obtained in terms of sum of squares (SOS). An example is provided to show the effectiveness of the approach.