An Improved Approach to Delay-dependent Stability Analysis and Stabilization for Takagi-Sugeuo Fuzzy Models with Time-delay

一種改良型之高木•菅野模糊型時延系統之時延相關強健穩定化準則

劉柄麟(Pin-Lin Liu)

《建國科大理工期刊》 31卷1期 (2011/10) Pp. 27-42

https://doi.org/10.6995/JSECTU.201110.0027

摘要

本論文旨在針對高木•菅野模糊型時延系統之時延相關穩定化準則提出改善之方法。首先提出高木•菅野模糊型時延系統之時延相關漸近穩定度之充分條件。基於線性矩陣不等式(LMI)求解最大允許延遲時間的問題。採用Lyapunov泛函數最佳化演算法設計迴授控制器推導出基於LMI的控制器設計方法。根據此充分條件，推導成一個凸優化問題，使用LMI工具箱求解器，可得到該系統的最大允許延遲時間(MADB)。文中舉例驗證與現有文獻結果相比較可得較寬廣的時間延遲範圍使得系統仍為漸近穩定。

關鍵字

高木•菅野模糊型時延系統 ； 線性矩陣不等式 ； 時延相關強 ； 積分不等式矩陣

並列摘要

This paper focuses on the improved approach problem for delay-dependent stability analysis and controller synthesis of T-S fuzzy systems with time delay. We first consider asymptotical stability conditions of fuzzy systems. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time delay, and are given in linear matrix inequalities (LMIs). An appropriate selection of Lyapunov-Krasovskii function and introduction of integral inequality approach (ⅡA) generalize asymptotical stability conditions. Next, we consider the stabilization problem with memoryless and delayed feedback controllers. The LMI optimization approaches are used to obtain a sufficient condition that is very easy to be checked by using the LMI Toolbox in Matlab. Based on them, we can obtain the maximum allowable delay bound (MADB). Finally, we give two examples that illustrate our results. We compare our conditions with other stability conditions and show our conditions are rather generalized.

並列關鍵字

T-S fuzzy systems ； linear matrix inequalities LMIs ； delay-dependent ； integral inequality matrix