Simultaneous Stabilization and Robust Control for Polynomial Nonlinear Systems Using SOS

In this paper, we discuss the simultaneous stabilization and robust control for a class of polynomial systems. By employing state-dependent polynomial Lyapunov functions, sufficient conditions for stabilization with and without H_infin performance are presented. These conditions can be verified by the recently developed technique named as sum of squares (SOS), which essentially is an LMI feasibility problem.