Stability analysis and design of a time delay estimation based control for a class of nonlinear uncertain systems

This paper presents a novel time delay estimation (TDE) based control for a class of nonlinear multiple-input-multiple-output (MIMO) uncertain systems. The design of the proposed control is given in a backstepping manner together with two key components: TDE, for estimating system nonlinearities and uncertainties; and nonlinear damping, for ensuring the closed-loop stability. An exact stability condition is established for the ultimate boundedness of the closed-loop tracking error via Lyapunov functions. There are two major merits of adopting the nonlinear damping. First, the closed-loop stability is guaranteed, despite time delayed terms and system nonlinearities and uncertainties; Second, the control performance is enhanced by dissipating the disturbing energy. The effectiveness of the proposed control is verified through experimental study with a two degree-of-freedom (DOF) robot manipulator.