第一部份, Takagi-Sugeno 模糊模型可完整地代表原始的非線性系統, 並且藉由Lyapunov 定理將問題轉為線性矩陣不等式, 此一簡單且兼具數理基礎和系統化步驟的特色成為本篇論文使用的主要原因。如上, 所以我們先建立一具耗散性的模糊化奇異攝動系統, 接著導入耗散性控制, 可藉由選取供應率(supplyrate) 的特點來處理各種性能問題, 之後再設計一分散平行補償控制器(PDC)利用狀態回饋控制來控制系統。
第二部分, 在最近幾年的模糊控制文獻中, 大部分研究主要著重於找出一共同P 矩陣來滿足二次Lyapunov 函數, 此一方法為充分但非必要條件且求解較保守(conservatism)。在此我們使用了波雅定理的代數性質來建立一組線性矩陣不等式, 此組線性矩陣不等式可求得出一二次穩定之不保守解(less conservativesolution), 進而漸進至系統穩定之必要條件, 在數理方面證明雙向的充要條件, 以工程的角度則可設計出使系統性能便好的控制器。

In this thesis, we propose a general quadratic dissipative state feedback control method to solve a stabilization problem for fuzzy singularlyperturbed system. The problem covers the bounded real, positive realand sector-bounded performance as a special case by choosing the corresponding
quadratic supply rate. Moreover, we also prove necessary
and sufficient conditions to state feedback controllers ensuring quadratic stability for Takagi-Sugeno fuzzy systems in theory. But our main objective is to generate a family of linear matrix inequalities based on an extension of P´olya’s theorem(a.k.a Matrix-valued P´olya’s heorem).
The proposed conditions are stated as progressively less conservative sets of linear matrix inequalities, allowing us to obtain a solution for the quadratic stabilizability problem whenever a solution exists.

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