Optimal sliding mode control for Delta operator system

The synthesis problem of optimal sliding mode control strategy is investigated for Delta operator system. Switching function is designed by quadratic performance index to guarantee the stability of the control system in the switching band. The optimal sliding mode controller for Delta operator system is designed by the discrete reaching law. The proposed strategy brings related conclusions of continuous time system and the discrete-time system into unified Delta operator system. Delta operator sliding mode control system not only can reach the region of the optimal sliding mode plane in finite time, and is stable in the sliding mode band in the end, but also decrease the system chattering effectively. Finally, the simulation result illustrates the feasibility and validity of the proposed strategy.