Optimal integral sliding mode control for a class of uncertain discrete-time systems

This paper considers the problem of sliding mode control for a class of uncertain discrete‐time systems. Firstly, an optimal control law for the nominal system is derived to satisfy linear quadratic performance index. And then, an optimal integral sliding surface is designed to ensure the robustness for sliding dynamics. By combining with the discrete reaching law, the existence condition of the sliding mode is proved, and the bandwidth of the quasi‐sliding mode is given. It is shown that the present method utilizes a lower control gain to attain stronger robustness and eliminate the chattering. Finally, illustrative simulation results are provided.