Abstract
In this paper, a sliding sector for discrete-time systems is defined based on a norm of the system state. Inside the sliding sector, the norm decreases without any control action. The discrete-time VSS control law is designed to move the system state from the outside to the inside of the sliding sector. The optimal control theory is used to design the sliding sector. The proposed VSS control method is applied to the control of the rotational inverted pendulum of the benchmark problem. The simulation results show its effectiveness
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