Robust exponential stabilization of underactuated mechanical systems in the presence of bounded disturbances using sliding mode control

This article addresses the robust exponential stabilization problem of underactuated mechanical systems in the presence of bounded external disturbances using sliding mode control. Based on the Lyapunov method, a sufficient condition for the existence of the smallest possible ball which bounds the reduced-order sliding mode dynamics, is first derived in terms of linear matrix inequality (LMI). A sliding mode controller is then synthesized to guarantee that system state trajectories are exponentially convergent to another ball with a prespecified  onvergence rate. A case study of the Pendubot is provided to illustrate the effectiveness of the proposed approach.