Our contribution is devoted to a further theoretic development of the attractive ellipsoid method (AEM). We consider dynamic models given by nonlinear ordinary differential equations in the presence of bounded disturbances. The resulting robustness analysis of the closed-loop system incorporates the celebrated Clarke invariancy concept (an analytic extension of the celebrated Lyapunov methodology). We finally obtain a new general geometric characterization of the AEM-based approach to the robust systems design. Moreover, we also discuss the corresponding numerical aspects of the proposed theoretical extensions of the method. The theoretic results obtained in this contribution are finally illustrated by a practically oriented computational example. © 2018 John Wiley & Sons, Ltd.