Robust and global stabilization of nonlinear systems

This paper investigates the robust and global stabilization problem of general nonlinear systems by introducing a variable index control approach. Variable index control laws can be derived based on a set of feasible multiple error indices, which always exist for general nonlinear systems, and the worst-case control strategy. The global stability and the robustness of the variable index control systems with bounded uncertainty are proved in the paper. The new approach can be applied to nonlinear systems which are not feedback-linearizable, and whose uncertainties are not required to satisfy any matching condition. The control actions are chatter-free. The feasibility of the variable index control approach has been demonstrated by design examples and numerical simulations