本文分別針對輸入大於輸出的嚴格真分線性系統和真分線性系統，提出了一種新的基於靜態零點配置的「增維方陣化」方法來代替「降維方陣化」方法，產生具有相等輸入和輸出的系統，並保留給定極小相位系統的原始輸出矩陣。新提出的零點配置方法可以始終將方陣系統的零點放置在所需的位置，以保持原有的極小相位特性，並確保得到的方陣系統仍是極小相位。結果表明，基於方陣系統的控制設計方法具有一定的實用價值。本文在方陣系統的基礎上，提出了四種新的等效輸入干擾估計方法：一、嚴格真分的連續時間系統（不含輸入輸出直接傳輸項），二、真分的連續時間系統（含輸入輸出直接傳輸項），三、嚴格真分的採樣數據系統，四、真分的採樣數據系統，分別有／沒有未知的匹配／不匹配干擾。即使對於沒有顯式擾動的系統，所提出的等效輸入干擾估計仍然可以改善伺服控制引起的隱式擾動。此外，對於具有劇烈變化的預定軌跡的被控系統，該方法不僅提高了系統的追蹤效能，而且使系統具有平滑的控制輸入。

Instead of the “squaring down” method, new static zero-assignment-based “squaring up” methods for strictly proper and proper linear systems which have more inputs than outputs have been respectively proposed in this thesis, to produce systems that have equal inputs and outputs and retain the original output matrix of the given minimum-phase (MP) system. The newly proposed zero-assignment method can always place zeros of the squared-up system at desired locations to preserve the original minimum-phase property and insure the resulting squared-up system is MP. As a result, some benefits of the square-system-based control design methodologies can be applied. Based on the squared-up system, four new equivalent input disturbance (EID) estimation methods are consequently proposed in this thesis for (i) strictly proper continuous-time systems (without the input-to-output direct transmission term), (ii) proper continuous-time systems (with the input-to-output direct transmission term), (iii) strictly proper sampled-data systems, (iv) proper sampled-data systems, respectively, with/without unknown matched/mismatched disturbances. Even for the system without explicit disturbances, the proposed EID estimation can still improve the implicit disturbance induced by the servo control. Furthermore, it not only improves the tracking performance but also induces a smooth control input for the controlled system with a drastic varying pre-specified trajectory.

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