本論文主要研究多項式模糊系統之靜態輸出回授控制器設計，使 用齊次多項式李亞普諾夫函數 (Lyapunov function) 及其對時間的導數 作為穩定條件，並同時滿足 H∞ 性能指標。本論文研究靜態輸出回授 是因為它比狀態回授能夠更廣泛的應用到實務上，而靜態輸出回授增 益設計，分別探討連續以及離散系統。連續系統中利用尤拉齊次多項 式定理建立李亞普諾夫函數 (Lyapunov function)，其形式為 V (x) = xT P (x)x = 1 xT ∇xxV (x)x g(g − 1) 離散系統為避免非二次齊次多項式李亞普諾夫函數 (Lyapunov function) 在其中發生問題，在本論文中將令李亞普諾夫函數 (Lyapunov function) 為 V ( x ) = x T P − 1 ( x ̃ ) x 其中 x ̃ 為系統狀態向量 x 裡不直接被控制器影響的系統狀態集合而 成。此限制可使後續電腦模擬時可行，內文中將詳細說明。 電腦模擬方面以平方和方法 (Sum-of-Squares) 來檢驗模糊系統的 穩定條件，並設計靜態輸出回授控制器。;In this thesis, we investigate H∞ control problem for both continuous- and discrete-time polynomial fuzzy systems, and to design static output feed- back controllers. The stabilization of the underlying systems can be proved via homogeneous Lyapunov method. This thesis studies static output feed- back control that is more appropriate in practical than state feedback con- trol. In continuous-time systems, Euler’s homogeneous polynomial theorem is used to formulate a Lyapunov function. It has the following form V (x) = xT P (x)x = 1 xT ∇xxV (x)x g(g − 1) In discrete-time systems, the Lyapunov function is formulated by V ( x ) = x T P − 1 ( x ̃ ) x where x ̃ are part of x that are not directly affected by the control input. This restriction is to avoid problems when doing simulation. The details will be described later. In numerical simulations, examples are solved via the sum-of-squares approach.
