The sum of squares(SOS) and the S-procedure techniques are used to analyze the local robust stabilization
problems for a class of polynomial systems with polytopic uncertainties. By using the SOS technique, the nonlinear control
problems are converted into convex SOS programming ones. And the S-procedure technique guarantees that the result holds
in a restricted region. Moreover, sufficient conditions are given for the robust stability analysis and robust stabilization control
of the systems based on the parameter dependent Lyapunov function. All these solvability conditions are formulated as a
constraint set of state dependent linear matrix inequalities, which can be solved by semidefinite programming relaxations
based on SOS programming. Finally, a numerical example verifies the effectiveness of the proposed method.