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Model reduction of high-order polynomial systems is considered. The main novelty of the paper is that the polynomial coefficients are assumed to be known only within given intervals. The resulted reduced system is characterized by a fixed-coefficients polynomial. First, the meaning of such a model reduction is defined. Then, applying a novel approach, the maximal "distance" (error) between the polygon in the complex plane which represents, at each frequency, the original uncertain system and the point which represents the resulted reduced-order fixed-coefficients system, is minimized. By a smart definition of this "distance" and by a formulation of the "closest" distance to the polygon as a "maximum" in some sense, the problem is formulated as linear semi-infinite programming with linear constraints, thus reducing significantly the computational complexity. A numerical example is provided.