Discrete-time sliding mode control for a class of underactuated mechanical systems with bounded disturbances

Abstract

This article addresses the problem of discrete-time quasi-sliding mode control for a class of underactuated mechanical systems in the presence of bounded external disturbances. Based on the Lyapunov stability method, a sufficient condition for the existence of a stable sliding surface is derived in terms of a linear matrix inequality (LMI). This condition also guarantees that the effects of external disturbances can be suppressed when the system is considered in the sliding mode. Moreover, in the induced sliding dynamics, all the state trajectories are exponentially convergent to a ball whose radius can be minimized. A robust discrete-time quasi-sliding mode controller is then proposed to drive system state trajectories towards the sliding surface infinite time and maintain it thereafter subsequent time. A case study of the Pendubot is provided to illustrate the feasibility of the proposed approach.