本論文係研究具有時間延遲的正向系統之穩定性分析及穩定化控制設計，研究的範疇為連續性的時間延遲系統。系統中的強健穩定度是一個良好的系統所必須要具備的。此外，在實際的系統中，另一個值得注意的問題是時間延遲的問題。由於實際系統中，狀態的傳遞需要時間，必然會有時間延遲的發生，而系統中含有區間不確定量因子，是本文的主要探討。
我們針對正向性與穩定性問題，推導出新穎且簡易的充分與必要條件，基於此條件設計出狀態回授控制器，便可確保系統之正向性與穩定性，再以前述之分析結果，利用線性規劃方法來尋找最佳化的控制器參數。最後以時間延遲的正向系統為數值範例分析，對此系統設計控制器，討論補償前與補償後系統性能之差異，經由模擬結果顯示，所設計的控制器是有效且適用的。

This thesis is concerned with stability and stabilization of time-delay interval and polytopic systems of the positivity constraints. Continuous-time time-delay system is discussed. The robust stability in the systems is a must for a good system. In addition, in the actual systems, another issue worth noting is the problem of time-delay. Due to the time required for the transmission of state in the actual systems, there will inevitably be a time-delay, and the system contains an interval uncertainty factor, which is the main discussion in this thesis.
For positive and stability analysis problems of systems, we derive some new sufficient and necessary conditions. Then based on these conditions, a linear programming method is applied to design controllers. Several examples, including practical examples and compartmental systems are given to demonstrate the effectiveness and applicability of the proposed methods.

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