Optimal integral sliding mode for uncertain discrete time systems

This paper proposes an optimal integral sliding mode control design method for a class of uncertain discrete-time systems. Firstly, the optimal control law on the nominal system is derived to satisfy linear quadratic performance index. And then, an optimal integral sliding mode is designed to ensure the stronger robustness for sliding dynamics. By combining with the discrete approach law, the existence condition of the sliding mode is proved, and the bandwidth of the quasi sliding mode is also derived. The present method utilizes a lower control gain to attain stronger robustness, and eliminate the chatter. Finally, a numerical example is given.