Application of Stability Criterion for Structure Systems

穩定準則在結構系統之應用

蕭鳳翔(F. H. Hsiao) ； 陳震武(C. W. Chen) ； 蔣偉寧(W. L. Chiang)

《中國造船暨輪機工程學刊》 22卷3期 (2003/08) Pp. 153-158

https://doi.org/10.29982/JTSNAME.200308.0005

摘要

本文提出一模糊模型的穩定準則並應用此準則於3個自由度的樓房。藉由T-S (Takagi-Sugeno) 模糊模型來表示的結構系統包含3個子結構系統且用此模型可針對複雜的非線性系統提出有效的表示形式。文中利用李雅普諾夫理論(Lyapunov's theory)推導一穩定準則並將穩定問題簡化成LMI (linear matrixinequalities) 問題。此穩定性分析可藉由LMI尋找共定矩陣來確立結構系統是否已達漸進穩定。最後，舉一例子，藉由數值模擬證實理論可行。

關鍵字

模糊系統 ； 相互交連系統 ； T-S模糊模型

並列摘要

The purpose of this paper is to apply a criterion of fuzzy model for the 3 degrees of freedom buildings. The structure
system consists of three floors represented by Takagi-Sugeno (T-S) type fuzzy models. T-S fuzzy models can provide an
effective representation of complex nonlinear systems. A stability criterion of the T-S type structure system is derived to
check if the system is asymptotically stable. Moreover, this stability problem can be reduced to linear matrix inequalities
(LMI) problems in terms of a common Lyapunov function. Solving linear matrix inequalities is a convex optimization
problem, and efficient interior-point algorithms are now available to solve this problem. Finally, a numerical example with
simulations is given to demonstrate the validity of the proposed approach.

並列關鍵字

Fuzzy Systems ； Interconnected Systems ； T-S Fuzzy Model