本論文以Takagi-Sugeno (T-S) 模式的模糊系統為基礎，提出探討模糊控制系統穩定性分析與性能改善的方法。首先，本論文對T-S模糊控制系統的架構及系統，做詳細的介紹。其次，本論文將針對目前T-S模糊控制系統的穩定性分析及設計瓶頸，分別提出以強健控制、最佳控制及Lyapunov穩定性分析的做法，並結合分群組設計技巧，來解決"需尋找共正定對稱P矩陣"確保T-S模糊控制系統穩定的問題，使得原來共正定對稱矩陣P要滿足所有模糊規則的問題簡化成系統強健及最佳設計等問題。此外，鑒於一般大型系統數學模式不易獲得，本論文亦建立一T-S模式為基礎的大型模糊系統模式，藉由Lyapunov方法推導獲得確保全系統穩定的充分條件。而存在的共正定矩陣問題亦可藉由分群組的技術解決。另外在系統性能方面，為增加設計彈性，藉由可控動態系統的建立及Lyapunov方法推導，不但可使得找共正定矩陣問題解決，並進一步提昇設計自由度。最後，本論文分別以實驗驗證與數值模擬的方式，來探討上述所提方法實際應用的可行性。 In this dissertation, several novel stability analysis techniques and systematic design procedures for the T-S model-based fuzzy control are proposed. After introducing the main problem and some essential properties of the T-S fuzzy system, the dissertation first propose a new approach to tackle the existing common P problem in T-S fuzzy model-based control system via some robustness criteria. The main merit of the approach is to overcome the difficulty of searching for a positive definite common P such that the global stability of the fuzzy system holds. For generalize applications, some useful properties can also be utilized to relax and enhance those stability criteria. Moreover, the conventional LQ approach is adopted to involve the design of T-S model-based fuzzy control system. Accordingly, the T-S fuzzy control system is possessed of properties having infinite gain margin and 60-degree phase margin. The stability of the T-S fuzzy system can also be guaranteed by the robustness of LQ controllers. Moreover, this dissertation also investigates an alternative stabilization for T-S fuzzy control system. Based on the T-S model in phase-variable canonical form, one can design the T-S fuzzy control system to fulfill different specification in different operating region. In the meantime, the existing common P problem in the T-S fuzzy system may just satisfy partial number of Lyapunov equations but not all Lyapunov equations. Hence, the stability of the T-S fuzzy control system can be guaranteed much easier. Furthermore, the fuzzy logic control design strategy is applied to the complex fuzzy large-scale systems. After choosing some operating point, the fuzzy large-scale systems is first decomposed by the T-S fuzzy model. Accordingly, some sufficient conditions are constructed for ensuring the stability of the global fuzzy system. The demanding for an exact model in traditional control strategy is then resolved. Several illustrative examples and simulations are used to demonstrate that the proposed approaches are effective and workable. Besides, the designing procedure for the T-S fuzzy system is systematic and simplified.
