本論文主要研究連續模糊控制系統的非二次穩定(non-quadratic stability) 條件，關於擴展狀態決定於高階的非二次李亞普諾夫函數，其函數形式是V(x) = 1/2(x^TP^(-1)(x)x)，其中條件P^(-1)(x) > 0取決於P(x)x 是一正定的梯度向量(gradient vector)。遺憾的是，此梯度向量P(x)x 是一非凸面體(nonconvex) 的問題。因此可控制的模糊系統之穩定性檢測條件，需要使用尤拉齊次多項式定理，並使用其定理之齊次性質與波雅定理(P?lya theorem) 之代數性質，以平方和方法(sum of squares) 去檢驗非凸面體問題，使得其模擬系統之空間解更寬鬆。最後，模擬其多項式模糊系統，表現出本論文提出之方法是有效的。 Extension of the state dependent Riccati inequalities to non-quadratic Lyapunov function of the form V(x) = 1/2(x^TP^(-1)(x)x), with P^(-1)(x) > 0 requires that P(x)x is a gradient of positive definite function. Unfortunately, the test of P^(-1)(x)x is nonconvex problem. Thus this thesis studies stabilization problems of the polynomial fuzzy systems via homogeneous Lyapunov functions exploiting the Euler’s homogeneity property and algebraic property of P?lya to construct a family of SOS polynomials that solves the nonconvexity problem and releases conservatism as well. Lastly, examples of polynomial fuzzy systems are demonstrated to show the proposed method being effective and effective.
