本篇論文主要研究連續時間強健(Robust)控制系統及離散時間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(P´olya 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
(P´olya 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。

In this thesis,we investigate non-quadratic ralaxation for continuous time robust control systems and discreate time fuzzy control systems,which are characterized by parameter-dependent LMIs (PD-LMIs),exploiting the algebraic property of P´olya Theorem to construct a family of finite dimensional LMI relaxations with righ-hand-side slack matrices that release conservatism.Certificates of convergence is proved.Lastly,numerical experiments to illustrate the advantage of relaxations,being less conservative and effective, are provided.

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