第一部分論述非線性系統轉換成廣義Takagi-Sugeno模糊系統後, 將其結合廣義動態輸出回授控制器, 並在上述架構下與圓定理整合, 求得雙線性矩陣不等式, 再簡化至動態輸出回授控制器, 求得在此系統架構下之二次穩定條件。 第二部份說明二次穩定LMI 檢測條件的演化, 從傳統LMI 檢測法到寬鬆矩陣變數和波雅定理的出現, 而重點在如何演進至平方和二次穩定檢測法。 第三部份討論圓定理與耗散性控制理論兩者的關聯性。 In this thesis, three topics are addressed. First, we investigate a general control problem via the Circle criterion borrowed from system theory; We show a fuzzy version of Circle criterion and then provide a synthesis result based on the Circle criterion, establishing closed-loop stabilizability for dynamic output feedback controllers and state-feedback controllers. Second, we show how to solve LMI representation numerically by SOSTOOLS. Third, we solve a stabilization problem for systems with sector-bounded nonlinearities at their input. Then, based on dissipative control and Circle criterion, we get the same stabilization conditions for a state feedback stabilizing controller. Finally, we integrate Circle theorem and dissipative control theorem into one unified structure.
