具狀態時延之T-S模糊系統的寬鬆穩定度分析─一個齊次多項式的方法

Relaxed Stabilization Conditions Analysis for T-S Fuzzy Systems with Time-Delay: A Homogeneous Polynomial Approach

方琮傑(Cone-Jie Fang)

指導教授 ： 蔡舜宏

國立臺北科技大學/機電學院/自動化科技研究所/碩士(2014年)

https://doi.org/10.6841/NTUT.2014.00735

摘要

本論文主要可分為兩個部分，第一部分為利用參數相依李亞普諾夫函數及齊次多項式技巧針對具狀態時延之T-S模糊系統推導其穩定條件。除此之外，為了使穩定條件更加鬆弛，加入波雅定理及寬鬆矩陣變數以降低其保守性。

第二部分主要為探討離散時間延遲系統之寬鬆穩定條件。本文中，我們利用權重相依李亞普諾夫函數，並且加入權重矩陣法使得穩定條件的保守性大幅降低。最後，提出幾個相關文獻的範例證明所提出的鬆弛穩定條件可提供較長之最大可允許延遲時間。

關鍵字

參數相依李亞普諾夫函數 ； 權重相依李亞普諾夫函數 ； 時間延遲 ； 波雅定理 ； 寬鬆矩陣變數 ； 權重矩陣 ； 齊次多項式

並列摘要

There are two parts in this thesis. In the first part, based on the delay-dependent Lyapunov function and homogenous polynomial technique, the stabilization condition is proposed for T-S fuzzy system with time-delay. In addition, by examining the relaxed stabilization condition, Pólya theorem and slack matrix variables are adopted to reduce the conservative of the proposed stabilization condition. Moreover, some examples are borrowed from the existing studies to demonstrate that the proposed method can provide the maximal allowable delay time than the other studies.

In the second part, the stabilization condition for discrete-time T-S fuzzy system with time-delay is explored. By utilizing the weighting-dependent Lypunov function and weighting-matrix method, the conservatism of stabilizations are reduced. Lastly, some numerical examples are illustrated to demonstrate that the proposed relaxed stabilization conditions can provide the maximal allowable delay-time than some studies.

並列關鍵字

Parameter-dependent Lyapunov function ； Weighting-dependent Lyapunov function ； Time-delay ； Pólya theorem ； Slack matrix variables ； Weighting-matrix ； Homogenous polynomial

參考文獻

[1]T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Trans. Syst., Man, Cybern., vol. SMC-15, pp. 116–132, Jan. 1985.

[2]K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. New York: Wiley, 2001.

[3]T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Trans. Syst., vol. 15, 1985, pp. 116-132.

[4]K. Tanaka, H. Yoshida, H. Ohtake, and H.O. Wang, "A sum-of-squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems," IEEE Transactions on Fuzzy Systems, vol. 17, no. 4, 2009, pp. 911-922.

[5]K. Tanaka, H. Ohtake, T. Seo, M. Tanaka and H.O. Wang," Polynomial fuzzy observer designs: A sum-of-squares approach," IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 42, no. 46, 2012, pp. 1330 – 1342.