Robustness analysis of uncertain nonlinear systems is often dominated by computationally expensive Monte-Carlo simulations, motivating the development of alternative approaches, including deterministic methods for worst-case assessment. An efficient solution approach is developed for a finite-horizon robustness analysis method that is based on a linear time-varying model along a nominal trajectory with quadratic constraints capturing nonlinear effects. The method leverages a transformed Riccati differential equation formulation with analytically optimized time-varying parameters to reduce computational complexity. Local quadratic constraints are iteratively refined using sparse grids. Application to Huygens’ atmospheric entry flight demonstrates accurate estimation of worst-case bounds with moderate
conservatism.