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In this paper, we use SOS (sum of squares) programming approaches to analyze the stability and robustness properties of the controlled pitch axis (6 state system) of a nonlinear model of an aircraft. The controller is a LTI dynamic inversion based control law designed for the short period dynamics of the aircraft. The closed loop system is tested for its robustness to uncertainty in the location of center of gravity along the body x-axis. Results in the form of stability regions about a trim point are computed and verified using simulations.