Variable Structure Control for Systems with Norm Bounded Uncertainty

In this paper, the problem of variable structure control for norm bounded uncertain systems is considered. Firstly, an exponential stability criterion is proposed for norm bounded uncertain systems. Then the sliding surface equation is given by using input matrix of system and variable structure control law is designed. This control law not only can guarantee the system arrive the sliding surface in finite time and also can assure the exponential stability of the reduced-order equivalent system dynamics restricted to the sliding surface. Finally, an example is presented to show the efficiency of this control law.