使用可變結構設計方法估測具備有界控制器之不確定模糊系統之漸進穩定範圍

ESTIMATION OF THE ASYMPOTOTIC STABILITY REGION OF UNCERTAIN FUZZY SYSTEMS WITH BOUNDED CONTROLLERS USING VARIABLE STRUCTURE SYSTEM DESIGN APPROACH

陳志杰(Chih-Chieh Chen)

指導教授 ： 龔宗鈞

大同大學/電機資訊學院/電機工程學系所/碩士(2010年)

摘要

在本論文中，針對不確定非線性系統探討其漸近穩定範圍預測的問題。我們以T-S模糊模型及可變結構控制技術去處理這類的問題。因此，具備有界滑動模式控制之不確定T-S 模糊系統的漸近穩定範圍預測問題被提出。為了簡化問題，我們針對這樣的系統做了狀態轉以達到系統降階的目的，並對轉換後的系統設計了一個滑動面。最後使用李亞普諾夫(Lyapunov)穩定性定理，漸進穩定範圍的預測可被獲得，經由模擬能夠論證我們所提出的論點。

關鍵字

漸進穩定區域 ； 可變結構系統 ； T-S模糊模型 ； 線性矩陣不等式 ； 李亞普諾夫穩定性定理

並列摘要

In this thesis, the problem of estimating the asymptotic stability region (ASR) of uncertain nonlinear systems is considered. Our approach is based on Takigi-Sugeno (T-S) fuzzy modeling method and variable structure control (VSC) technique. Thus, the problem of estimating the ASR of uncertain T-S fuzzy systems with bounded sliding mode controllers is proposed. To simplify the problem, we use a state transformation to reduce the system order of the T-S fuzzy systems. Then we design the sliding surface for the transformed system. Using the Lyaponov stability theorem, the ASR can be estimated. Simulation results are presented to verify the effectiveness of the proposed scheme.

並列關鍵字

asymptotic stability region ； variable structure system ； T-S fuzzy model ； linear matrix inequalitie ； Lyaponov stability theorem

參考文獻

[1]V. I. Utkin, “Variable structure systems with sliding modes,” IEEE Transactions on Automatic Control, vol. 22, no. 2, pp. 212–222, Feb. 1977.

[2]H. H. Choi, “An explicit formula of linear sliding surfaces for a class of uncertain dynamic systems with mismatched uncertainties,” Automatica, vol. 34, no 8, pp. 1015–1020, Aug. 1998.

[3]M. Zohdy, M. S. Fadali, and J. Liu, “Variable structure control using system decomposition,” IEEE Transactions on Automatic Control., vol. 37, no. 10, pp. 1514–1517, Oct. 1992.

[4]W. J. Wang, G. H. Wu, and D. C. Yang, “Variable structure control design for uncertain discrete-time systems,” IEEE Transactions on Automatic Control., vol. 39, no. 1, pp. 99-102, Jan. 1994.

[5]C. Lin, Q. G. Wang, and T. H. Lee, “Stabilization of uncertain fuzzy time-delay systems via variable structure control approach,” IEEE Transactions on Fuzzy Systems., vol. 13, no. 6, pp. 787–798, Dec. 2005.