本計畫透過廣義KYP 引理，研究連續時間、線性非時變系統之有限頻段H-infinity 輸出回授控制器設計問題，並著重在問題中加入不同複雜度的控制器限制條件，例如降 階、強穩定、分散式、PID 控制器設計以及靜態輸出回授設計。在全頻段控制領域這些 議題並不陌生，然而在有限頻段控制領域目前仍僅有極少數研究成果。鑑於尤拉參數式 的複雜形式，不利用於上述問題。植基於我們所推導出較不保守的性能條件，我們將修 改全頻段H-infinity 控制器設計的4-block 問題轉換技巧，應用互質分式表式法，將閉回 路有限頻段輸出回授控制器設計問題轉換為有限頻段“濾波器”設計問題。另外，我們 也將把前述研究方法推廣延伸至具不確定參數的系統(採用Δ-P-K系統架構表示)，提出 有限頻段mu 合成方法。對於上述所有問題，我們將提出線性矩陣不等式形式的有解條 件，研擬演算法，執行數值模擬，並與現有相關方法作比較，來驗證所提方法的效果。 最後，我們將致力於雛型系統硬體驗證平台之建置，以實體驗證所設計控制器之效能。 In this project, we will investigate the H∞ output feedback control problem in finite-frequency domain for continuous-time linear time-invariant systems via generalized Kalman-Yakubovich-Popov (GKYP) lemma, with emphasis on imposing different controller complexity such as reduced-order, strongly stabilizing, decentralized, PID, and static output feedback upon the designs. The problems are not new in full-frequency domain but only very few results have been addressed in finite-frequency domain. Owing to the complicate mathematical representation of the Youla controller parameterization, which is not useful for solving the aforementioned design problems, we will derive less conservative performance conditions based on which we will modify the 4-block transformation technique used in H∞ controller synthesis in full-frequency domain, and use coprime fractional representation to convert the finite-frequency output feedback controller synthesis problem into filtering like problem. In addition, extension of the above results to systems with uncertain parameters will also be studied. By adopting the Δ-P-K controller synthesis paradigm, we will propose a new mu synthesis with emphasis on restricted frequency ranges. We will derive solvability conditions in terms of linear matrix inequalities (LMIs) for the aforementioned control problems, propose state-space computational algorithms, conduct numerical simulations, and make comparison with some of the existing methods. Finally, we will devote ourselves to the establishment of the hardware verification plateform in order to verify the efficacy of the proposed controllers.
