Discrete-time Variable Structure Control

Abstract

This chapter presents some discrete-time variable structure (VS) control design algorithms with sliding sectors and then proposes a discrete-time VS controller with an invariant sliding sector. The invariant sliding sector is an invariant subset of the state space determined by a linear and a quadratic functions on the state variable. To ensure the invariance, a VS control law is implemented. Inside the sector with the VS control law, a Lyapunov function keeps decreasing. If the state is inside the subset in some time instance, then the VS control input will let the state remain inside. A discrete-time VS controller with the invariant sliding sector for discrete-time systems is designed such that the state is moved into the sector in finite steps and stays there from then on. The resultant VS control system is quadratically stable as there exists a Lyapunov function which decreases in the state space. Simulation results are given to show the efficiency of the proposed design algorithm of the discrete-time VS controller.