arXiv:2604.08521v2 Announce Type: replace-cross Abstract: We study the robustness to plant-model mismatch of nonlinear systems in closed loop with (discounted) optimal controllers designed for a nominal model, with quadratic stage costs across finite and infinite horizons. By combining Lyapunov analysis with a unifying relaxed dynamic programming framework, we establish conditions that guarantee robust stability alongside improved suboptimality bounds compared to existing literature. A key step in our analysis is proving that stability counteracts time-accumulated error growth due to plant-model mismatch, yielding robustness bounds that hold uniformly across all prediction horizons.