動態輸出回授控制平方和穩定分析

Dynamic Output Feedback Stability Analysis via SOS

廖偉証(Wei-cheng Liao)

指導教授 ： 羅吉昌

國立中央大學/工學院/機械工程學系/碩士(2011年)

摘要

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。

關鍵字

線性矩陣不等式 ； Takagi-Sugeno 模糊模型 ； 扇形有界非線性項 ； 廣義動態輸出回授控制器 ； 平方和 ； 圓準則 ； 耗散性控制

並列摘要

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.

並列關鍵字

circle criterion ； sum of squares ； T-S fuzzy model ； generalized dynamic output feedback controller ； dissipative control ； sectorbounded nonlinearity ； Linear matrix inequality

參考文獻

[2] 萬嘉仁, “寬鬆耗散性模糊控制- 波雅定理,” 國立中央大學, 碩士論文, 民國97 年.

[3] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modelling and control,” IEEE Trans. Syst., Man, Cybern., vol. 15, no. 1, pp. 116–132, Jan. 1985.

[4] M. Sugeno and G. Kang, “Structure identification of fuzzy model,” Fuzzy Set and Systems, vol. 28, pp. 15–33, 1988.

[5] K. Tanaka and M. Sugeno, “Stability analysis and design of fuzzy control systems,”Fuzzy Set and Systems, vol. 45, pp. 135–156, 1992.

[6] W. Haddad and D. Bernstein, “Explicit construction of quadratic Lyapunov functions for the small gain, positive, circle and Popov theorems and their application to robust stability. Part II: discrete-time theory,” Int’l J. of Robust and Nonlinear Control, vol. 4, pp. 249–265, 1994.