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

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.