An improved SOS-based stabilization condition for uncertain polynomial systems

State-feedback stabilization problem for polynomial systems using rational Lyapunov functions is revisited in this paper. Here, we proposed a new sufficient condition for the controller design, which is convex in the decision variables and can be solved using the sum-of-squares (SOS) technique. The new sufficient condition separates the system matrices and the Lyapunov matrices, and hence parameterization of the resulting controllers is independent of the Lyapunov-matrix variables. The proposed approach enables us to construct robust controller for uncertain polynomial systems using parameter-dependent Lyapunov functions.