Sliding mode control design in multi-input perturbed discrete-time systems

Variable structure control (VSC) design in multi-input discretetime systems has two main difficulties: one is the satisfaction of the hitting condition and the other is the handle of the state trajectory in (quasi) sliding mode. The former is caused by the multiple inputs of the system, and the latter is caused by that the perturbation exists and the sliding surface is a bounded region but not only the hyperplane S = 0. This paper overcomes the above two difficulties successfully and designs the sliding region, the sliding control U_s and the hitting control Uj such that the system’s state can reach the sliding hyperplane (in fact it is a region) and finally moves to the origin.