Quasi-smooth control of chained systems

Abstract

The problem of exponential stabilization for high-order chained systems with two control inputs is addressed and solved using a particular class of discontinuous dynamic state feedback control laws. The proposed method substantially improves the existing results in several respects. Firstly no limitation on the plant initial conditions needs to be imposed; secondly the method can be used to stabilize a much larger class of nonlinear systems which cannot be exponentially stabilized by smooth control; finally, although Lyapunov stability cannot be ensured, the closed loop controlled system possesses a weak Lyapunov stability property.