本文介紹機械與結構系統之質塊-阻尼-彈簧模型，並探討此模型之傳輸零點分佈、最小相位特性與最小相位強健性問題。藉由適當的非線性映射及應用根軌跡技術，吾人成功地證明出：滿足充分條件B=CTΓ之比例阻尼型(proportional damping)質塊-阻尼-彈簧系統，其傳輸零點與極點：在複數左半s-平面之特定圓及負實軸線段上有交錯分佈(interlacing)的現象。

　　在文獻中已證實：滿足B=CTΓ之質塊-阻尼-彈簧連續時間系統具有最小相位特性。值得再深入探討的是：該系統經取樣後，是否仍保有最小相位特性？在本文中吾人證實：滿足B=CTΓ之模式阻尼型(modal damping)質塊-阻尼-彈簧系統經過取樣後，仍是最小相位系統。值得注意的是：此特性與取樣頻率無關。

　　此外，質塊-阻尼-彈簧不確定性系統，其最小相位特性之強健性問題亦是值得探討的主題。因此，吾人將推導其保持最小相位特性所能容許之最大擾動範圍。由於此最小相位強健性問題，係直接以二階動態型式表示之，故可得到最小維度之擾動矩陣，進而獲得較精確之結果。

　　最後，吾人延伸探討具有仿線性參數不確定性(affine parametric uncertainty)之狀態空間系統，決定該系統保有最小相位特性所能容許之最大擾動範圍。文中，吾人利用線性分式轉換(linear fractional transformation)，以減少求結構化奇異值(structured singular value)之矩陣的維度，並降低數值計算量。

　The mass-dashpot-spring models of mechanical and structural systems are introduced in this work. It is aimed to investigate the transmission zeros distribution, the minimum phase property and minimum phase robustness for a mass-dashpot-spring system. By virtue of an appropriate nonlinear mapping and the root-locus technique, it is verified that the transmission zeros interlace with poles on a specific circle and the nonpositive real axis segments of the s-plane for a mass-dashpot-spring system with proportional damping and B=CTΓ.

　In literature, a continuous-time mass-dashpot-spring system with B=CTΓ was shown to be minimum phase. It is worthy to investigate whether the corresponding sampled-data system still exhibits minimum phase property. In this work, the sampled system of a modal damping mass-dashpot-spring structural dynamics with sufficient condition B=CTΓ is verified to be minimum phase. Notably, this property is independent of the sampling period.

　In addition, it is desirable to know how robustly an uncertain mass-dashpot-spring system maintains the minimum phase property. To this end, the allowable margin of perturbations is derived to guarantee minimum phase property of the uncertain system. For the sake of obtaining less conservative results, the perturbation matrix with a minimal dimension is directly derived on the basis of a second-order dynamical equation.

　At last, the uncertainties margin for a state-space system with affine parametric uncertainties is determined. The minimum phase property of the uncertain system is guaranteed within the uncertainties margin. Based on the linear fractional transformation, the matrix sizes involved in the computation of structured singular value are significantly reduced to improve computational burden.

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