Design of variable structure control system by using the vectorLyapunov function method

摘要

The objective of this paper is to present a simple design methodof a variable structure controller for systems with nonlinearuncertainty. The proposed method is based on a kind of a boundary layermethod and can eliminate chattering. The control law is given by sum ofa linear feedback and a saturation type nonlinear state feedback, thatis, a linear feedback in the boundary layer and sum of an affinefeedback outside it. So, it is a very simple control law. The proposedcontrol law guarantees exponential stability of O solution if there isno disturbance. If disturbance exists, it guarantees ultimate boundness.The ultimately bounded region is inside the boundary layer, in which thecontrol is a linear feedback. In the proposed design method, stabilityis analyzed by using the vector Lyapunov function approach