Global sliding-mode control for companion nonlinear system with bounded control

Based on feedback linearization, quasi-time-optimal control and sliding-mode control theory, a kind of quasi-time-optimal, continuously time-varying sliding-mode for robust control of nonlinear uncertain systems subject to input constraint is presented. The proposed sliding surface can adapt it to the initial conditions of the system and the controller can be composed of two parts: one part is used to turn the nonlinear system into linear system by feedback linearization, and the other part is used to realize the quasi-time-optimal control for feedback linearized system. By this means, insensitivity of the system to external disturbance and parameter uncertainties is guaranteed from the very beginning of the proposed control action, and the system error convergence rate can be greatly increased. The advantages of the proposed scheme are indicated by comparison with the Bartoszewicz´s scheme (1996), and the Lyapunov theory is used to prove the existence of a sliding mode on the surface