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 Title: 模糊系統觀測控制器設計─齊次多項式尤拉法;Observer and Controller Design of Fuzzy Systems via Homogeneous Euler′s Method Authors: 林承緯;Lin,Cheng-wei Contributors: 機械工程學系 Keywords: 非二次穩定;平方和;參數相依齊次多項式;Takagi-Sugeno模糊系 統;尤拉齊次多項式定理;泰勒級數;Non-quadratic stability;Sum of squares;Homogeneous polynomially parameter-dependent (HPPD) functions;T-S fuzzy systems;Euler′s Theorem for Homogeneous Functions;Taylor-Series Date: 2015-07-30 Issue Date: 2015-09-23 15:12:42 (UTC+8) Publisher: 國立中央大學 Abstract: 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 controllerdue to their dependability. The main contribution in this thesis isnon-quadratic stability of continuous fuzzy systems, which is modeledby Taylor series method. And we can solve the inequations derivedfrom non-quadratic Lyapunov function and its time gradient. Theform of extension from the state dependent Riccati inequalities tonon-quadratic Lyapunov function isV(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 gradientof V(x,e), we introduce Euler′s homogeneous polynomial theoremto derive the SOS condition and solve for the observer and controllerwith sum-of-squares approach. Appears in Collections: [機械工程研究所] 博碩士論文

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