Sampled‐Data Based Second‐Order Discrete‐Time Sliding Mode Control via Output Feedback

ABSTRACT This article proposes a second‐order discrete‐time sliding mode controller (DSMC) by only using sampled‐data information of the system output. On one hand, different from the continuous‐time sliding mode control, the finite‐time stability of the closed‐loop system under DSMC is usually not kept due to the limited sampling frequency. On the other hand, in the output feedback framework, the second‐order sliding mode observer cannot independently estimate the internal state of the system if there exist unknown mismatched term and unknown time‐varying coefficient of the control input. To solve the above problems, a joint design strategy of second‐order discrete‐time sliding mode observer and sliding mode controller based on the “non‐separation principle” is proposed. The stability and robustness of the closed‐loop system is analyzed based on the Lyapunov design method. Finally, simulation example verifies the correctness of the theory.