本論文中，主要探討含有不確定性因素的二階時變微分系統穩定度分析。由於在實際的環境中，不管儀器再精密或是實驗環境再理想，一定會有不可避免的擾動或是參數變動的問題，因此，這些不確定性因素的考量，對於系統本身而言，是不可或缺的。 本論文分別對系統的領導係數矩陣分別為奇異與非奇異矩陣做探討，利用矩陣以及不等式的性質，而推導出一個新的充份指數穩定條件，並與文獻的例子做比較，證明本論文所提出的定理比文獻中的結果更不具保守性。 基於此指數穩定條件，利用動態迴授來設計控制器，並結合最佳化方法來尋找控制器參數。最後以一個實際的二階系統為例，對此系統設計控制器，並分別對時間響應以及頻率響應做分析，討論補償前與補償後系統性能的差異，結果顯示補償後的性能優於未補償的系統，證實所設計的控制器是有效的。 This thesis is concerned with exponential stability analysis of second-order time-varying differential systems with nonlinear uncertainties bounded by Lipschitz constants. The systems with singular and non-singular leading coefficient matrices are both discussed. New sufficient conditions for exponential stability of the above mentioned uncertain systems are derived and the upper bounds of allowable nonlinear uncertainties are obtained. Furthermore, the proposed result is less conservative than the results of literatures. It is shown that proposed criterion is superior to the literatures and has better improved. Then using proposed criterion combines with optimization method to design controller. Both singular and non-singular illustrative examples are shown to compare uncompensated system with compensated system. According to simulation results, after adding the controller can let the system become stable. Finally, a practical example is shown to demonstrate that using proposed criterion to design controller can improve the performances. In frequency domain analysis, after adding the controller, the resonant frequencies are eliminated. In time domain analysis, three experiments are implemented. All of these results show that the controller can improve the performance of system.
