Design of Approximation Law for Discrete-time Variable Structure Control Systems

This paper presents two approximation laws of sliding mode for discrete-time variable structure control systems against defects existing in the exponential approximation law and the variable rate approximation law. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems, the switching between approximation laws does not exist, the stability of origin can be ensured and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of approximation law proposed, the problem of system control input being restricted is also considered, which is very important in practical system. Finally one simulation example is given to show the effectiveness of the two approximation laws proposed