平方和模糊系統觀測器設計 -齊次多項式法

SOS-Based Fuzzy Observer Dsigns -Homogeneous Polynomial Approach

章為盛(Wei-sheng Chang)

指導教授 ： 羅吉昌

國立中央大學/工學院/機械工程學系/碩士(2014年)

摘要

本論文主要研究連續及離散模糊觀測系統的非二次穩定
(Non-quadratic stability) 條件，關於擴展狀態決定於非二次李亞普諾
夫函數，其函數形式是V(e)=1/2e^TQ(e)e，其中條件Q(e)> 0 取決於Q(e)
是一正定的梯度向量(gradient vector)。遺憾的是，此梯度向量Q(e)
是一非凸面體(nonconvex) 的問題，因此可觀測的模糊系統
之穩定性檢測條件，需要使用尤拉齊次多項式定理，並使用其定理之
齊次性質，以平方和方法(Sum of squares) 去檢驗非凸面體問題，使
得其模擬系統之空間解更佳。最後，模擬其多項式模糊系統，表現出
本論文提出之方法是有效的。

關鍵字

非二次穩定 ； 平方和 ； 參數相依齊次多項式 ； 模糊系統 ； 尤拉齊次多項式定理

並列摘要

In this thesis, we extend of the state dependent Riccati inequalities to non-quadratic Lyapunov function of the form V (e) = 1/2e^TQ(e)e where Q(e) > 0 requires that Q(e) is a gradient of positive definite function.Unfortunately, the test of Q(e) is nonconvex problem. Thus this thesis studies stabilization problems of the polynomial fuzzy systems via homogeneous Lyapunov functions exploiting the Euler’s homogeneity property to construct a family of SOS polynomials that solves the nonconvexity problem and releases conservatism as well. Lastly, examples of polynomial fuzzy systems are demonstrated to show the proposed
method being effective and effective.

並列關鍵字

Non-quadratic stability ； Sum of squares ； Homogeneous polynomially parameter-dependent (HPPD) functions ； T-S fuzzy systems ； Euler’s Theorem for Homogeneous Functions

參考文獻

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