本論文藉著矩陣不等式的方法來研究離散時間奇異系統的可容許性與嚴格耗散性之分析與狀態回授控制器的設計問題。藉由一些輔助矩陣以及一個大於零的常數，吾人提出一個新的不等式條件，並證得此不等式是有解的與離散時間奇異系統是可容許且嚴格耗散的為等價關係。當給定大於零的常數時，此不等式條件成為線性矩陣不等式，因而在設計狀態回授控制器時比目前已知文獻中的不等式條件更容易求得數值解。此外吾人更將上述結果推廣到當所考慮系統的數學模型包含了範數有界不確定項時的情況。在理論說明之後並輔以數值範例來說明控制器增益的設計結果。

In this thesis, we study the admissibility and the strict dissipation analysis of the discrete time singular systems and its associated state feedback controllers design by means of matrix inequality techniques. By the introduction of some auxiliary matrix and a positive constant, a new set of matrix inequality conditions is proposed and its feasibility is proved to be equivalent to the admissibility and strict dissipativeness of the discrete-time singular systems. The matrix inequality condition becomes a linear one when the constant variable is given. This makes the numerical solution of state feedback controller design much easier than the solution of a set of nonlinear matrix inequality conditions appeared in the literatures. We also extend this result to the case when mathematical model of the considered singular systems contains the norm-bounded uncertainties. Some numerical examples are given to illustrate the design of the required state feedback gain matrices.

摘要.................................................................i
表次.................................................................v
圖次................................................................vi
符號表.............................................................vii
第一章 緒論..........................................................1
1-1節 背景與動機...............................................1
1-2節 論文架構.................................................2
第二章 幾個矩陣性質..................................................3
第三章 離散時間奇異系統的可容且嚴格耗散之分析與設計..................5
3-1節 系統描述.................................................5
3-2節 奇異系統之可容性與嚴格耗散性定義.........................6
3-3節 奇異系統之可容且嚴格耗散分析.............................8
3-4節 狀態回授控制器設計......................................18
第四章 離散時間奇異系統的強韌可容且嚴格耗散之分析與設計.............23
4-1節 系統描述................................................23
4-2節 奇異系統之強韌可容且嚴格耗散分析........................23
4-3節 狀態回授控制器設計......................................31
第五章 數值模擬.....................................................36
第六章 結論.........................................................45
參考文獻............................................................46

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