本論文討論以矩陣型式表示多樣的複數平面圖形區域，以及正多項的低階控制器設計。本文中所討論穩定區域的圖形包含一維度、二維度以及多維度的組合圖形如：平移平面、圓形、橢圓、拋物線及其任意組成之區域圖形。在多項式方法的控制器設計中，我們以設定的區域為閉迴路極點放置的目標，並給定我們所想要的控制器階數以求解一組符合的控制器。最後我們以淡江大學航太系UAV實驗室所設計的無人飛行載具為例，做縱向運動之高度及姿態保持控制設計。 This thesis discusses the matrix representations of various complex stability regions and the designs of fixed-order controllers using positive polynomials. Stability regions presented in this thesis include one dimensional, two dimensional and their combinations. Regions such as shifted half plane, circle, ellipse, parabola, and union of regions are narrated and collated. A stabilizing control problem with low-order controller to satisfy additional constraints on the closed-loop pole location is explored in the thesis. A H-infinity control problem using positive polynomial concepts is also investigated. The longitudinal auto-pilot designs for a low-speed uninhabited experimental aircraft are presented to illustrate the fixed-order controller design using positive polynomials.
