在自動控制領域中，對於一個符合可控條件的線性非時變系統，若要處理讓系統狀態回到原點之問題(regulation problem)，最經典的設計方法即為極點配置法。其利用狀態回授的方式，將極點放置在任何期望的位置上，使系統狀態漸近收斂到原點。若要進行追蹤控制(tracking problem)，必需在狀態回授控制器裡，加入一個追蹤項。但傳統上，其只可確保非零常數訊號的追跡，對於時變訊號，則會有明顯的相位差產生。本文針對線性非時變系統，探討其追蹤問題，並提出一追蹤控制器，其即使對快速時變訊號，也沒有相位差問題。
以上設計是考慮系統並無受到外擾的狀況下，若系統包含外擾，其設計就相當有挑戰性了。本文進一步對具有匹配式外擾的線性非時變系統，提出追蹤控制器，其中使用滑動控制的概念來容忍外擾的影響，讓系統狀態皆能收斂到時變的期望軌跡。
當系統狀態無法得知，上述的控制方法都無法實現。可建構觀察器來估測系統狀態，並使用估測的狀態計算控制量，以達到控制目的。由於在系統受到外擾下設計控制器就已非常不易，若系統狀態又無法得知，在加入觀察器後，其控制器設計難度會大幅增加。如果再將其設計擴展到多輸入多輸出系統，必然更是困難重重。最後，本文針對多輸入多輸出線性非時變系統，結合狀態觀察器，設計一強健追蹤控制器，來容忍外擾的影響，以達到漸進收斂的性能。其中利用Lyapunov穩定度法則來證明其系統穩定性，並以電腦模擬驗證此控制法為可行。

For a completely controllable LTI system, the pole placement design is perhaps the most renowned control method for regulation problems. It allows the closed loop poles to be placed at desired locations by full state feedback so that the system states may converge to the origin asymptotically. As for the tracking problems, an additional term should be included in the controller to provide sufficient driving activities. However, it is only valid for the tracking of step signals, and a significant lag can be observed for the tracking of a time-varying trajectory. In this thesis, the tracking problem is studied in detail for a LTI system and a state feedback tracking controller is proposed so that the states may follow fast time-varying trajectories asymptotically.
The above designs are under the disturbance-free condition. With the presence of external disturbances, the problem becomes challenging. This thesis further proposes a tracking controller for a LTI system subject to matched disturbances. A robust term based on the sliding control is introduced to tolerate the effect of the disturbances so as to give convergence of the system states to the desired trajectories.
If the states are not available, the above strategies are not feasible. The observers can thus be constructed to estimate the system states so that we may replace the actual states in the controller by using these estimates. However, inclusion of the state observer will further complicate the design and the controller derivation becomes more difficult. If the structure is extended to MIMO systems, the development is extremely complex. Finally, this thesis proposes a robust tracking controller for a MIMO LTI system based on state observers to tolerate external disturbances. The Lyapunov theory is utilized to prove system stability and computer simulations are performed to justify feasibility of the designs.

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