Under review for publication in the Journal of Guidance, Control, and Dynamics.In lieu of extensive Monte-Carlo simulations for flight control verification, sum-of-squares programming techniques provide an algebraic approach to the problem of nonlinear control synthesis and analysis. However, their reliance on polynomial models has hitherto limited the applicability to aeronautical control problems. Taking advantage of recently proposed piecewise polynomial models, this paper revisits sum-of-squares techniques for recovery of an aircraft from deep-stall conditions using a realistic yet tractable aerodynamic model. Local stability analysis of classical controllers is presented as well as synthesis of polynomial feedback laws with the objective of enlarging their nonlinear region of attraction. A newly developed synthesis algorithm for backwards-reachability facilitates the design of recovery control laws, ensuring stable recovery by design. The paper's results motivate future research in aeronautical sum-of-squares applications
