本博士論文針對T-S模糊系統提出了三個放寬的穩定化準則與兩個成本保證控制之應用。前兩個放寬準則是針對離散型T-S模糊系統所提出的。一開始我們先將操作狀態空間(operation state space)分割成幾個子區間，並根據這些子區間，將T-S模糊系統轉換成一個相等的切換式模糊系統(switching fuzzy system)。 接著，基於相對應於子區間之區間型片段式李亞普諾夫函數(regional type piecewise Lyapunov function)，並考慮連續兩個狀態間可能的子區間轉換，對離散型T-S模糊系統提出了前兩個放寬準則。基於最小型片段式李亞普諾夫函數(minimum type piecewise Lyapunov function)與隨著片段式李亞普諾夫函數轉換之切換式模糊控制器，針對連續型T-S模糊系統提出了第三個放寬準則。在此放寬準則中的某些條件包含了據有特別雙線性項(bilinear term)之雙線性矩陣不等式(bilinear matrix inequality)。根據文獻，路徑跟隨法(path-following method)對於此種雙線性矩陣不等式非常有效，因此其被用於求得此放寬準則之解。而T-S模糊系統的兩個成本保證控制之應用則為自我平衡之腳踏車(self-sustaining bicycle)系統與天車(overhead crane)系統。一開始我門先將腳踏車與天車的動態分別轉換成不確定建模T-S模糊系統(T-S fuzzy system with model uncertainty)與模糊描述型系統(fuzzy descriptor system)。接著，針對被轉換後之不確定建模T-S模糊系統與模糊描述型系統設計了成本保證模糊控制器(guaranteed cost fuzzy control)。由於腳踏車與天車系統據有一些實際的限制，於是在設計成本保證控制器時，輸入與狀態限制也一並被考慮了。據作者所知，此博士論文為第一個針對不確定建模T-S模糊系統與模糊描述型系統，考慮輸入與狀態限制，而設計成本保證模糊控制器之研究。並且模擬的例子展現出了放寬準則之放寬性與成本保證控制應用的有效性。 This dissertation proposes three relaxed stabilization criteria and presents two applications of guaranteed cost control for T-S fuzzy systems. The first two relaxed stabilization criteria are proposed for the discrete T-S fuzzy systems. The operation state space is divided into several sub-regions, and then the T-S fuzzy system is transformed into an equivalent switching fuzzy system according to the sub-regions. Subsequently, based on the regional type piecewise Lyapunov function corresponding to the sub-regions, the relaxed stabilization criteria are derived by considering all possible transitions. The third relaxed stabilization criterion is proposed by applying the minimum type piecewise Lyapunov function and the switching fuzzy controller for the continuous T-S fuzzy systems. Some conditions of the relaxed stabilization criterion are represented by bilinear matrix inequalities which contain some particular bilinear terms. According to the literature, the path-following method is very effective for this kind of bilinear matrix inequality problem, hence it is utilized to obtain solutions of the criterion. The two applications of guaranteed cost control for T-S fuzzy systems are the self-sustaining bicycle and overhead crane. The nonlinear dynamics of the self-sustaining bicycle and overhead crane is exactly transformed into a T-S fuzzy system with model uncertainty and a fuzzy descriptor system respectively. Guaranteed cost fuzzy controllers are then design for the transformed T-S fuzzy system and fuzzy descriptor system. Since the self-sustaining bicycle and overhead crane have some practical constraints, the input/state constraints are also considered in the design. To the author's knowledge, the studies in this dissertation are the first studies of guaranteed cost control with input/state constraints for the T-S fuzzy system with model uncertainty and fuzzy descriptor system. Moreover, simulated examples are given to show the relaxation of the relaxed stabilization criteria and the effectiveness of the guaranteed cost control applications.
