正值系統之 H-infinity 控制器設計

H-infinity Controller Synthesis for Positive Systems

潘咨融(Tzu-Jung Pan)

指導教授 ： 周永山

淡江大學/工學院/電機工程學系碩士班/碩士(2016年)

https://doi.org/10.6846/TKU.2016.01031

摘要

本文研究離散時間、線性、非時變正值系統之動態輸出回授H∞控制器設計問題。首先針對輸出矩陣具有特定形式之正值系統，本文推導出以線性矩陣不等式（linear matrix inequality, LMI）與線性不等式組成之充要條件，其甚至適用於控制器為降階與具結構限制的情形。針對更具一般性之正值系統，本文提出相似的充分條件以及兩階段式之設計演算法。另外，更進一步地以類似論點延伸至另一種狀態空間之控制器合成問題。最後，模擬結果證實了本文所提方法是有效的。

關鍵字

正值系統 ； 輸出回授 ； 降階 ； 結構化控制器 ； 線性矩陣不等式

並列摘要

This paper is concerned with the H-infinity dynamic output-feedback stabilization of discrete-time positive linear time-invariant systems. It is first shown that for a class of positive systems whose output matrix has a particular form, necessary and sufficient condition is derived in terms of a set of linear matrix inequality (LMI) and linear inequalities, even if the output feedback controllers are of reduced-order and/or have structural constraints. Analogously, for the more general case, sufficient conditions of similar form are also derived and a two-stage algorithm is developed. Further extension to the synthesis problem in a different state space is also made by similar arguments. Finally, simulation is conducted that establishes the effectiveness of the proposed methods.

並列關鍵字

positive systems ； output-feedback ； reduced-order ； structured controller ； linear matrix inequality

參考文獻

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