Variable structure control for a class of nonlinear systems with mismatched uncertainties

A scheme to stabilize nonlinear time-varying systems with both matched and mismatched uncertainties is proposed in this paper by switching between two control laws: a first-order sliding-mode control and a second-order sliding-mode control. Based on this idea, a variable structure control algorithm is designed for a class of second-order systems. The closed-loop system is globally or locally asymptotically stable. It has been proven that the stability region has relation with the order of the boundary function and the region can be obtained by solving an inequality. The uncertainty considered in this work is also more general than those in the existing works.