本論文主要是利用投影法來處理控制系統的相關問題。我們先將矩陣投影的原理，推導至複變數域中。根據所導衍的投影運算子，可以解複數矩陣不等式的問題。 根據李亞普諾夫(Lyapunov)穩定性理論，我們先提出不確定連續系統的穩定性準則，然後藉由複數矩陣不等式，進而將準則延伸至極點配置的問題。此外，對於不確定的離散系統，亦提出了穩定性和D-穩定性的判定準則，其準則亦可用矩陣不等式的方式來描述。根據投影法，我們提出了有效的數值演算法來分析系統的強健穩定性。若加入狀態迴授控制器，我們更提出了一些有效的設計方法。 最後，我們將探討利用T-S 模型來表示的模糊系統其穩定性的問題。根據複數矩陣不等式，其穩定性的論點，將被延伸至滿足特定要求的穩定性。這樣我們則可運用所提出的投影演算法則，來判定系統的特定穩定性條件。若加入平行補償器 (PDC)，亦提出了幾種設計的方法。最後利用數值例和模擬結果來論述所提出方法的可行性和有效性。 In this thesis, the projection method will be involved for solving the concerned control problems. The projection philosophy is extended to complex number field. By the derived projection operators, a set of complex LMI can be solved. Based on Lyapunov stability theorem, we first present a stability criterion for linear uncertain systems. By involving the complex LMI, the criterion can be extended to the problem of the pole assignment in a specific region. Furthermore, we similarly present the stability and D-stability criteria for discrete uncertain systems. Thus, by the projection scheme, the projection algorithm is then proposed to analyze the stability. By involving the state feedback control, we further propose some design methods for linear uncertain systems. Finally, the stability issues of the fuzzy systems, described in Takagi-Sugeno’s (T-S) fuzzy model, are discussed. Based on the complex LMI, the stability issue can also be extended to a prescribed stability region. By involving the PDC (Parallel distributed compensation), we further propose some design methods for the overall fuzzy system. Some numerical examples and simulation results are given to demonstrate the validity and feasibility of our methods.
