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This paper gives a sufficient condition for a robust control problem in terms of minimax polynomial optimization. A minimax problem is investigated by using sum of squares relaxation of parametric polynomial optimization problems. The sufficient condition can be exact from the Positivstellensatx. The minimax approach is adopted for robust stability analysis of parameter-dependent systems and an equivalent stability condition is also given from quadratic version of distinguished representation of positive polynomials. Finally, a numerical example is shown.