本篇論文主要研究連續時間強健 (Robust) 控制系統及連續時間 Takagi-Sugeno(T-S)模糊控制系統的非二次(non-quadratic)穩定寬鬆條件; 我們利用波雅定理(Polya Theorem)的代數性質加上寬鬆矩陣變數(slack matrix variables)來建立一組寬鬆的線性矩陣不等式(LMI)，因為非二次(non-quadratic)穩定的分析加上寬鬆矩陣變數 (slack matrix variables) 的使用，使得此組線性矩陣不等式(LMI)的求解保守性更進一步的降低，亦即當使用波雅定理(Polya Theorem)時，齊次多項式的階數不用太高，就可以找到解，這是本論文最大的優點；最後會提出幾個例子來證明我們理論的優越性。關鍵字：強健(Robust)控制系統 Takagi-Sugeno(T-S)模糊控制系統、 非二次 (non-quadratic)穩定、 波雅定理 (Polya Theorem)、寬鬆矩陣變數(slack matrix variables)、 線性矩陣不等式 (LMI)In this thesis, we investigate non-quadratic ralaxation for continuous-time robust control systemsand continuous-time fuzzy control systems, which are characterized by parameter-dependent LMIs (PD-LMIs), exploitingthe algebraic property of Polya Theorem to construct a family of finite-dimensional LMI relaxations with righ-hand-sideslack matrices that release conservatism. Lastly, numericalexperiments to illustrate the advantage of relaxations, being less conservative and effective, are provided.it keyword: Robust control systems; Takagi-Sugeno fuzzy control systems; Non-quadratic relaxations;Parameter-dependent LMIs (PD-LMIs); Polya Theorem; Slack matrices; Linear matrix inequality (LMI).
