Combining state estimator and disturbance observer in discrete‐time sliding mode controller design

In response to a multiple input/multiple output discrete‐time linear system with mismatched disturbances, an algorithm capable of performing estimated system states and unknown disturbances is proposed first, and then followed with the design of the controller. Attributed to the fact that both system states and disturbances can be estimated simultaneously with our proposed method, the estimation error is constrained at less thanO(T) as the disturbance between the two sampling points is insignificant. In addition, the estimated system states and disturbances are then to be used in the controller when implementing our algorithm in a non‐minimum phase system (with respect to the relation between the output and the disturbance). The tracking error is constrained in a small bounded region and the system stability is guaranteed. Finally, a numerical example is presented to demonstrate the applicability of the proposed control scheme.