Robust Finite-Time Stabilizers for a Connected Chain of Nonlinear Double-Integrator Systems

Abstract

In this paper, the robust finite-time stabilization problem is addressed for a wide group of fully actuated nonlinear systems containing dependent double-integrator subsystems in the presence of unbounded uncertainties. Based on the nonsingular terminal sliding mode control, three types of stabilizers are proposed to steer the system states to zero within adjustable convergence finite times. Moreover, several inequalities are obtained to determine the conservative upper bounds for these convergence finite times. To clarify the applicability of the suggested stabilization methods, a finite-time tracking problem for robotic manipulators is discussed and handled by applying three introduced stabilizers. Finally, a numerical simulation related to this tracking problem is provided.