本論文主要研究連續模糊系統的非二次穩定(non-quadratic stability) 條件，以泰勒級數建模得出模糊系統，且以非二次的李亞普諾 夫函數(Lyapunov function) 及對時間的變化率作為穩定的條件，對 於決定擴展狀態的高階李亞普諾夫函數，其形式為 V(x,e)=[x e][adj(Q(x)) 0;0 U(e)][x;e] 而使用尤拉齊次多項式可以排除V(x,e)對時間t 微分所產生Q(x) 之 微分項，再以平方和方法(Sum-of-Squares) 來檢驗模糊系統的穩定條 件，並設計出其觀測器及控制器。 由於觀測器與控制器的相依性，分離設計並不容易，本論文將以 限制條件分段解析，並找出有條件下的分離設計方法。;It′s not easy to separate the synthesis of observer and controller due to their dependability. The main contribution in this thesis is non-quadratic stability of continuous fuzzy systems, which is modeled by Taylor series method. And we can solve the inequations derived from non-quadratic Lyapunov function and its time gradient. The form of extension from the state dependent Riccati inequalities to non-quadratic Lyapunov function is V(x,e)=[x e][adj(Q(x)) 0;0 U(e)][x;e]. To overcome the di erential terms of Q(x) derived from time gradient of V(x,e), we introduce Euler′s homogeneous polynomial theorem to derive the SOS condition and solve for the observer and controller with sum-of-squares approach.
