本篇論文是研究狀態回饋控制以及 H∞ 性能的模糊控制穩定性分析 ， 本論文將分成兩部分來進行討論 ，
第一部份先推導(控制)系統滿足 Lyapunov 穩定的檢測條件 。
第二部分考慮干擾的影響 ， 推導出使受控系統滿足 H∞ 穩定的檢測條件 。
對於一個具非線性特徵的 Takagi-Sugeno(T-S) 模糊系統 ， 在新的寬鬆充分條件之下保證其穩定 。
無論是連續或者離散時間的模糊(控制)系統都是用相似的方法(檢測條件 LMIs)來探討 。
本篇論文是針對一個前件部相依的 Lyapunov 函數(premise-dependent Lyapunov function)來探討 T-S 模糊系統的穩定條件 ，
而以前的文獻一般都是用單一矩陣 P(common P) 來推導所需的檢測條件 。
對於穩定與性能分析以及控制器的設計目前都是用 LMI 以及數值分析來處理運算 ，
這些採用前件部相依的 Lyapunov 函數(premise-dependent Lyapunov function)
經數理證明及電腦模擬的結果都比現存文獻採用單一矩陣 P(common P) 的結果寬鬆 。

In this paper, sufficient LMI conditions for the H∞ state feedback
control synthesis of fuzzy control systems consisting of Takagi-Sugeno
fuzzy models are proposed for continuous- and discrete-time fuzzy sys-
tem in a unified manner. Based on a premise-dependent Lyapunov func-
tion, we release the conservatism that commonly exists in the common
P approach. Particularly, the restriction embedded in continuous-time
systems on derivative of μ is removed by introducing Lie derivative to
the Lyapunov approach. It is shown that the slack variables employed in
this paper provide additional feasibility in solving the H∞ stabilization
problem of fuzzy control systems. Consequently, the stabilization condi-
tions are shown to be more relaxed than others in the existing literature.
Numerical simulations appear promising for the proposed method and
illuminate the reduction of conservatism clearly.

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