This paper investigates new ways of accounting for saturations in nonlinear dynamic inversion schemes. Because of its high practical interest, the particular case of rate limitations will receive a special attention here. The central contribution of the paper consists of showing how the nonlinear control problem can be rewritten in a standard form, strongly inspired by the robustness analysis framework. More precisely, standard dynamic-inversion-based controllers are viewed in this paper as particular solutions to a more general nonlinear compensation scheme. Various strategies are then proposed to solve the problem, among which multi-channel H_∞ design approaches - for which new optimization tools were recently made available - will play a key role. In a second step, anti-windup optimization is also considered to further improve the control laws. The proposed methodology is illustrated by a realistic aircraft control design example.