某些非線性受控系統中都含有未知的元素，諸如未知系統參數(unknown parameter)或系統內部改變的不確定性(uncertainty)，因此很可能造成控制系統的工作性能下降，並且使得針對系統追蹤性能的目標不易達成，甚至造成閉迴路系統不穩定。

H∞控制器的特色是可使受控體在不確定外擾作用及系統參數變動情況下，仍可維持系統的穩定性與強健性。而模糊控制器的優點則是可以使用知識庫的模糊規則來設計控制器，不需要明確的數學模式。本文結合模糊理論與H∞控制理論的優點，而發展出穩定且具有高性能的模糊-H∞控制器。並且利用線性矩陣不等式(LMIs)來驗證閉迴路系統是否穩定，以及驗證可否達到奇異值小於一定數值之性能要求。

最後，本文針對機械手臂系統作為電腦模擬控制對象，來驗證所設計之模糊-H∞控制器之可行性。經由模擬結果顯示可達到不錯的追蹤性能，證明確實能使系統有良好的追蹤性能，並能有效降低外系統矩陣不確定性因素的影響。

A nonlinear dynamic system usually contains some uncertainties, such as unknown system parameters or uncertainties, which may make desired performance hard to be achieved or even cause the close-loop system unstable.

The feature of H∞ controller is to keep the system stable and robust under the presence of system disturbances or uncertainties. The merit of fuzzy control is to apply fuzzy knowledge base and fuzzy controller is to apply fuzzy knowledge base and fuzzy rules on its control design, which doesn’t require exact math model. In this paper, we will combine fuzzy theory with H∞ theory to develop a Fuzzy-H∞ controller which has high performance. And we will use linear matrix inequalities (LMIs) to attest whether the close-loop system is stable and to achieve.

Finally, a nonlinear robot system is studied as an example in this research to attest the feasibility of the proposed Fuzzy-H∞ controller. The computer simulation results reveal that the designed Fuzzy-H∞ controller in this example can achieve the desired objectives with good tracking performance by effectively rejecting the uncertain matrices of system in this nonlinear robot system.

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