本論文探討兩個有關於強健性控制理論的主題。第一個主題探討滑動模式控制系統中的強健性控制器設計方法，藉由線性矩陣不等式的數學理論，分別發展出三種功能不同的強健性滑動模式控制器設計方法。其結果顯示，於滑動模式控制設計問題中，藉箸解一組聯立矩陣不等式，可設計出兼具強健穩定與強健性能的滑動模式控制器。本文所發展出來的設計方法，可適用於受到干擾且帶有耦合或不耦合不確定性的系統。此外，本文並建立一種逼近模式控制器以排除滑動模式控制系統中所產生的不良振顫效應。更進一步，本文發展出一種以狀態觀測器為基礎的逼近模式控制器，系統的強健性能要求仍能滿足。在第二個主題中，利用強健控制理論中的結構性奇異值理論，本文發展出一套分析複數區間矩陣穩定性的方法。基於此種方法架構，文中提出了多項複數區間矩陣、實數區問矩陣、複數區間多項式及實數區問多項式的穩定性判別法則。此外，文中提出一個有關於複數區間矩陣在控制系統上的應用，其結果有助於參數化不確定系統的研究。對於前述提出的各種設計及分析方法，文中亦提出了許多範例予以模擬說明。

　In the dissertation two topics are investigated regarding to the robust control theory. One topic is the design of robust controllers for sliding mode control systems. A linear matrix inequality technique is developed for the design of both sliding mode and reaching phase control laws. It is shown that by solving a set of LMIs, the switching surface can be designed such that the dynamics in the sliding mode achieve robust stability and bounded L2 gain performance with respect to matched and unmatched uncertainties in the presence of disturbances. Furthermore, a smooth reaching phase control law is presented to eliminate the undesirable chattering effect and maintain the robustness property all the time. Finally, a smooth observer based control law is developed to maintain the robust performance of a system in the case that not all of the states are accessible. In the second topic, a robustness analysis formulation, based on the structured singular value techniques, is proposed to study the stability problem of a complex interval matrix. Accordingly, explicit criteria for testing the Hurwitz stability of complex interval matrices, real interval matrices, complex interval polynomials and real interval polynomials are all constructed regarding to the proposed formulation. Besides, an application of complex interval matrices to the design of a control system is presented. Several simulations are given to illustrate the aforementioned design and analysis methods.

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