A New Finite Time Convergence Condition for Super-Twisting Observer Based on Lyapunov Analysis

A new convergence condition is proposed for the super-twisting sliding mode observer in this paper, where Lyapunov stability analysis is used as the main method to get the new convergence condition. The super-twisting sliding mode observer is designed to obtain unknown system states of the second order nonlinear system with bounded uncertainties and disturbances. By involving a quadratic Lyapunov function, the Lyapunov approach is applied to the stability analysis of the super-twisting observer, from which a new convergence condition is obtained to guarantee the finite time convergence of the observer. Simulation results of a pendulum and a rigid manipulator are included to demonstrate the effectiveness of the new convergence condition.