Stability Analysis of Takagi-Sugeno Fuzzy Systems with Time-Varying Delay: Delayed Decomposition Approach

高木‧菅野模糊型時延系統之穩定度分析：時延分解法

劉柄麟(Pin-Lin Liu)

《建國科大理工期刊》 33卷1期 (2013/10) Pp. 39-57

摘要

本論文，基於李亞普諾夫函數，推導出新的穩定性準則於其有時變延遲高木‧菅野模糊型時延系統。籍由李亞普諾夫函數來建構強健性穩定準則，將延遲函數的微分上界加入Lyapunov-Krasovskii泛函來降低準則的保守性。針對具有快速變動的時變延遲高木‧菅野模糊型時延系統也可直接處理，確保強健性穩定在最大允許上界的區間內。本論文的主要貢獻如下：1.利用積分不等式和自由權矩陣結合Lyapunov-Krasovskii泛函於具有時變延遲高木‧菅野模糊型時延系統之穩定度問題。利用牛頓－布尼茲公式中各項的關係，首次對此系統之強健穩定度提出時延相關的強健穩定性準則。2.利用時延分解結合Lyapunov-Krasovskii泛函方法，探討了此系統的穩定性。通過對時延進行分解，使得每一部分均依不同的Lyapunov泛函，分別獲得了系統時延相關的穩定性充分條件。

關鍵字

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

並列摘要

In this paper, new stability criteria of Takagi-Sugeno (T-S) fuzzy systems with time-varying delays based on Lyapunov functional will be derived. Furthermore, the T-S fuzzy systems with time-varying delays with large fast time-varying delays will be explored. The upper bound of the derivative of delay function will be incorporated into Lyapunov-Krasovskii functional such that the conservatism of the criteria can be reduced and the robust stability of the T-S fuzzy systems with time-varying delays will be guaranteed. A less conservative sufficient condition has been derived by integral inequality approach and free distribution parameters for increasing allowable delay interval and reducing positive contribution of the derivative of delays in the linear matrix inequalities (LMIs). The main highlight in this paper can be summarized as follows: 1. The robust stability problem for T-S fuzzy systems with time-varying delays is investigated by utilizing integral inequality approach and free weighing matrices combined with Lyapunov-Krasovskii functional. The method employs free weighting matrices to express the relationships between the terms in the Leibniz-Newton formula, and to obtain delay-dependent stability criteria. Numerical examples are given to show less conservatism compared with some existing ones [2, 3, 6, 8, 9, 10, 13, 15, 16, 17, 21]. 2. By developing a delayed decomposition approach, information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities (LMIs). Then, based on the Lyapunov method, delay-dependent stability criteria are devised by taking the relationship between terms in the Leibniz-Newton formula into account. Criteria are derived in terms of LMIs, which can be easily solved by using convex optimization algorithms.

並列關鍵字

Fuzzy system models ； Delay decomposition ； Time-varying delay ； Linear matrix inequalities ； LMIs ； Maximum admissible upper bound ； MAUB