強健正向系統的穩定度分析與控制器設計

Stability Analysis and Controller Design for Robust Positive Systems

李宗庭(Tsung-Ting Li)

指導教授 ： 莊堯棠

國立中央大學/資訊電機學院/電機工程學系/碩士(2011年)

摘要

本論文係研究正向系統之穩定性分析及穩定化控制設計，研究的範疇包含連續時間與離散時間兩大系統，系統中含有的區間跟凸形不確定量因子，是本文的主要探討之列。針對穩定性與正向性分析問題，而推導出新的充份與必要條件，基於此條件，搭配狀態迴授來設計控制器，便可應用於控制系統的穩定化設計上。利用前述之分析結果，配合線性歸劃方法來尋找控制器參數。最後以實際的正向系統為例，對此系統設計控制器，討論補償前與補償後系統性能的差異，經由模擬結果顯示，所設計的控制器是有效且適用的。

關鍵字

線性歸劃 ； 狀態迴授 ； 正向系統

並列摘要

This thesis is concerned with stability and stabilization of interval and polytopic systems with the positivity constraints. Both continuous-time and discrete-time are discussed. For stability analysis and stabilization problems of those systems, we derive some new conditions. Then based on these conditions, a linear programming method is applied to design controllers. Several examples, including compartmental systems and Leslie systems are given to demonstrate the effectiveness and applicability of the proposed methods.

並列關鍵字

positive systems ； linear programming ； state feedback

參考文獻

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