摘要
在這篇論文中，我要討論的是隨時間變動的週期離散系統，不只系統隨時間變化，每個時間系統的形式（size）也是隨時間不同。首先我簡單的描述Kalman canonical decomposition所運用的手法，此為整篇論文運作的基形。接下來將要討論的系統運用指導教授林文偉老師及郭岳承學長的方法改寫為forward和backward 兩個部分以便於觀察、控制。並定義forward和backward 兩個子系統及隨時間變動的週期離散系統的可達性及可觀測性，而由定義給予可達性及可觀測性的一些等價性質，並證明其等價成立。在有了明確的定義後，由於等價條件的類似性質，運用Kalman canonical decomposition的手法將forward和backward 兩個子系統minimal realization，透過瞭解子系統，以達到分析隨時間變動的週期離散系統的目的。由於整個理論架構都只有用到基本的矩陣運算，未來可將其寫成演算法，便於電腦運算。

In this paper we define the reachability and observability of
periodic descriptor system with time-varying size,and deduce some
equivalent properties from the definitions of the reachability and
observability,and moreover minimal realization of the system.

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