López-Martínez, M.Acosta Rodríguez, José ÁngelCano, J.M.2025-08-062025-08-062010-10López-Martínez, M., Acosta Rodríguez, J.Á. y Cano, J.M. (2010). Non-linear sliding mode surfaces for a class of underactuated mechanical systems. IET Control Theory and Applications, 4 (10).https://doi.org/10.1049/iet-cta.2008.0583.1751-86441751-8652https://hdl.handle.net/11441/176016This study presents a new non-linear sliding surface to control a class of non-minimum phase underactuated mechanical systems, taking into account uncertainties in their physical parameters. The non-linear surface is designed through a fictitious output, which provides the minimum-phase property and allows to prove stability using Lyapunov theory. The non-linear surface is based on the fictitious output and augmented with a non-linear external controller designed using the Lyapunov theory. The present approach assures exponential stability of the equilibrium point and robust stability to parametric uncertainties, avoiding the appearance of non-desired phenomena, as limit cycles. Two pendulum-like examples inside the class are thoroughly analysed and solved, that is, the pendulum on a cart and the inertia wheel pendulum. Performance, time response and parametric robustness are shown through simulations. © 2010 The Institution of Engineering and Technology.application/pdf18 p.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Lyapunov methodsMechanical engineeringMechanicsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1049/iet-cta.2008.0583