H∞控制理論是近三十年來控制理論界的傑作，但當雜訊來自於特定頻段時，直接應用H∞控制理論有時效果不佳，所以後來發展迴路整形(loop shaping)技術，引入權重函數(weighting function)來輔助設計。但適合權重函數的選擇不易，並且會增加控制器階數，增添硬體實現上之複雜度。因此本論文針對此種H∞迴路整形技術進行改良，另外也應用Iwasaki等人提出的廣義KYP (Generalized Kalman–Yakubovic–Popov, GKYP)引理，推導控制閉回路系統指定頻段性能的直接設計方法。 本論文針對離散時間不確定系統研究指定頻段濾波器與控制器之設計問題。我們推導出符合有限頻段性能要求的LMI設計條件式，以達到單頻段與多頻段性能之控制目的。其中，綜合運用不同理論可推導出許多有趣的成果，例如，不管有無引入權重函數，濾波器或控制器階數可預先設定。另外，濾波器型態可為無限脈衝回應(Infinite Impulse Response, IIR)以及有限脈衝回應(Finite Impulse Response, FIR)兩種典型的形式。本論文針對單輸入單輸出(single-input single-output, SISO)單頻段以及多頻段濾波器設計情形進行詳細討論，並以一致的技巧推廣至多數入多輸出(multi-input multi-output, MIMO)情形與強健控制器設計。 The Robust H∞ control is a masterpiece control theory in the past three decades. However, when applied to band-limit noise attenuation, it sometimes does not lead to satisfactory performance. The so called loop shaping method was derived to assist the design via introducing weighting functions. Nevertheless, selection of an appropriate weighting function is hard. Furthermore, it increases the order of controllers, and thus increases the hardware implementation complexity. Therefore, this thesis gives new method which improves the H∞ loop shaping method in the controller order aspect. In addition, we provide a direct method to this sort of problems. This thesis investigates the problems of filter and controller syntheses in finite frequency domain for uncertain discrete-time systems. We derive LMI conditions for the problems in both single-band and multi-band cases. The proposed methods offer flexibility in several aspects. For examples, the order of the filters and controllers can be assigned a priori; the type of filters can be either infinite impulse response (IIR) or finite impulse response (FIR). This thesis studies the single-input single-output (SISO) robust filter design in both single band and multiple bands in details. Then the results are extended to multi-input multi-output (MIMO) case and the case of robust controller design.
