A stabilizing control scheme is proposed for 2D polynomial nonlinear systems based on negative root
placement. Free polynomial is introduced to overcome the demerit of non-uniqueness description of system state matrix, which reduces the conservatism of solution for control synthesis. The problem of negative root placement is transmitted into positive polynomial validation problem. By the technique of polynomial decomposition, controller design problem is finally solved numerically by semidefinite programming tools. Stabilizing control for four types of 2D polynomial systems is discussed based on the addressed technique. Simulation results show the effectiveness of the presented method.