在設計控制器時，由於有許多不確定性與外擾會對響應造成影響，因此控制器需具有極佳的強健性，方能達成想要的控制目標。
　　順滑模態控制(sliding mode control)具有極佳的強健性且應用容易，故被廣泛的應用在控制領域。而高階順滑模態控制(high order sliding mode)則可視為是傳統順滑模態控制的延伸，它同樣也具有良好的強健性，更重要的是它需要的系統狀態較傳統的順滑控制少，所以高階順滑控制具有較高的實用性。
　　本文主要針對一具有外擾的離散系統探討。將傳統一階離散順滑控制加以延伸，提出了一個二階順滑控制方法。並用Lyapunov穩定準則證明在有限外擾的狀況下，狀態會進入二階順滑面，即 與 進入邊界層中。由研究結果得知其狀態響應皆符合預期，且可達成控制的目標，這亦顯示所提出的離散二階順滑控制方法的適用性。

To achieve the required system performance, the control system should robust to system uncertainties and disturbances. The sliding mode controller can be designed systematically with robustness to matched uncertainties. Therefore, it has been widely applied to many theorical studies and industrial applications.
The high order sliding mode controller can be considered as an extension of conversional sliding mode controller with less state information required and can suppress or reduce chattering due to the controller output. This make the high-order sliding mode controller more realizable then the conversional sliding mode controller.
In this thesis, discrete systems with disturbances are considered. An approach to design 2-order discrete sliding mode controller is proposed. The result can be extended to the high order cases. Using the Lyapunov stability criterion, the resulting system is guaranteed to stay around the desired sliding surface with a specific boundary. The performance of the proposed control system can be achieve, the design objective which indicate its feasibility of the proposed discrete high-order sliding mode controller.

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