具狀態時延之T-S模糊中立系統的寬鬆穩定條件

Relaxed Stabilization Conditions for T-S Fuzzy Neutral Systems with State Delay

孫震(Chen Sun)

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(2013年)

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模糊控制系統推導其二次穩定條件。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。並提出幾個相關文獻的範例來證明所提出的方法較其它文獻所提出之方法可提供系統更長的延遲時間。
第二部分主要是為探討具參數不確定性及外在干擾之中立系統之 控制之寬鬆穩定條件。本文中，我們利用齊次多項式特性及克羅內克乘積，並且加入寬鬆條件使得保守性降低。最後以一數值範例驗證所提方法之優越性及有效性。

關鍵字

平行分散補償控制器(Parallel distributed compensation, PDC) ； 參數相依李亞普諾夫函數(Parameter-dependent Lyapunov function) ； 狀態時延(State delay) ； 波雅定理(P&oacute ； lya theorem) ； 擴充矩陣(Augmented matrix) ； 寬鬆矩陣變數(Slack matrix variables) ； 中立系統(Neutral system)

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 quadratic stabilization condition is proposed for T-S fuzzy system with state delay. In addition, by examining the relaxed stabilization condition, Pólya theorem and slack matrix variables are adopted. 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 relaxed stabilization condition and control for T-S uncertain fuzzy neutral system with disturbance is explored. By utilizing the property of homogenous polynomial technique, Kronecker product and slack matrix variables, the relaxed stabilizations, being less conservative are provided. Finally, a numerical example is illustrated to demonstrate that the feasibility and effectiveness of the proposed control scheme.

並列關鍵字

Parallel distributed Compensation (PDC) ； Parameter-dependent Lyapunov function ； State delay ； P&oacute ； lya theorem ； Augmented matrix ； Slack matrix variables ； Neutral system

參考文獻

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