本論文主要研究齊次多項式尤拉法應用於切換式模糊控制器設計，以泰勒級數建模產生模糊系統，並使用片段式李亞普諾夫函數(piecewise polynomial Lyapunov function) 作穩定性分析，其高階李亞普夫函數型式為V (x) = min_1 <=l<= N(V_l(x)) ，其中V_l(x)=x^T*P_l(x)*x，N 為分段個數，根據dot(V(x))<0，做穩定性條件分析，在求解的過程中，片段李亞普諾夫函數V_l(x) 對時間微分會產生Pl(x) 之微分項，其化簡過程過於繁瑣複雜，為避免此問題，引用尤拉齊次法，再以平方和方法檢驗穩定度條件，並設計出控制器。;In this thesis, it is mainly to research piecewise fuzzy controller design by homogeneous polynomial Lyapunov Euler method. We use Taylor series to model the fuzzy system, and implement the analysis of stability by piecewise polynomial Lyapunov function,which has the following form:V(x)= min_1 <=l<= N(V_l(x)) and V_l(x)=x^T*P_l(x)*x. Due to the fact that dot(V_l(x))=dot(x_T)*P_l(x)*x+x^T*dot(P_l(x))*x+x^T*P_l(x)*dot(x), the dot(P_l(x)) will yields complicated form to implement stablility condition. To avoid this problem, we propose a homogeneous polynomial function method and utilize Euler’s theorem for homogeneous function. The next, we solve the stabilization problem under consideration by the method of sum of squares and design its corresponding controller.
