Robust decentralized global asymptotic tracking control of a class of nonlinear mechanical systems

In this paper, a RISE type of tracking controllers for a class of nonlinear mechanical systems is proposed. The proposed chattering-free controller provides global asymptotic tracking in the presence of external disturbances. The proof of global asymptotic stability is based on a novel approach to the construction of a Lyapunov function which is parameterized by a time-varying function of reference and disturbance vector. The explicit conditions on the controller gains to ensure global asymptotic tracking are obtained. The simulation results on a system of three inverted pendulums interconnected by two springs illustrate the performances of the proposed controller.