The current practice to validate flight control laws relies on applying linear analysis tools to assess the closed loop stability and performance characteristics about many trim conditions. Nonlinear simulations are then used to provide further confidence in the linear analyses and also to uncover dynamic characteristics, e.g. limit cycles, which are not revealed by the linear analysis. This paper reviews analysis techniques which can be applied to nonlinear systems described by polynomial dynamic equations. The proposed approach is to reduce the analysis problems to a sum-of-squares optimization problem which can then be solved with freely available software. These techniques can fill the gap between linear analysis and nonlinear simulations and hence can be used to provide additional confidence in the flight control law performance.