在本文中，我們將針對具有輸入式不確定的系統來設計一個可以追蹤參考輸入之H∞-強健控制器。輸入式不確定在於系統狀態空間方程式的輸入矩陣，其具有已知的上下限邊界，此不確定因素將使系統追蹤上產生不確定的擾動，還有可能造成系統的不穩定。

　　H∞-控制系統的特色是可以使受控體在不確定的外擾及系統參數變動的情況下，仍可維持系統的穩定與強健性，透過設定權重函數來使擴增系統的靈敏度函數、互補靈敏度函數及控制能量函數的奇異值圖擁有良好的形狀。

　　對於擴增系統使用黎卡迪方程式，求解出H∞-控制增益，所得的狀態回授控制要使系統在輸入式不確定的干擾下能達到H∞-控制的穩定與強健性。然後使用迴路函數整形的方法，來求得H∞-觀測增益，希望使輸出回授控制也擁有良好的性能。

　　為了驗證以上的H∞-控制理論，在本文中將以直流無刷伺服馬達為系統進行模擬，設定輸入式不確定矩陣的大小，其使外加電壓產生干擾。以求解出的H∞-控制器做追蹤和性能的模擬。

　In this thesis, we are trying to design a robust H∞-controller being capable of tracking reference input for uncertain system with parameter uncertainty in the input matrix. The parameter uncertainties appearing in the input matrix of a system state-space equation have known upper and lower bounds and may cause the system unstable.

　The character of an H∞-control law is that it can ensure the closed-loop system stable while guaranteeing the system robustness to the uncertain exogenous inputs and the plant uncertainties. By selecting suitable weighting functions in the H∞-formulation, we can shape the system sensitivity, power transfer and the complementary sensitivity functions in the s-domain to ensure the system stability and robustness.

　The uncertainties in the system input matrix is assumed to be bounded in a specific form given in this research. The loop transfer recovery (LTR) technique is applied to the H∞-control problem containing the input matrix uncertainties to propose the H∞/LTR methodology in this thesis.

　To test the feasibility of the proposed H∞/LTR control law, a DC brushless motor with parameter uncertainty in the system input matrix is simulated under the interference voltage. Simulation results reveal that the desired system performance can be achieved by using the proposed control strategy while guaranteeing the closed-loop stability and robustness.

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